almost automorphic solutions for stochastic differential equations driven by levy noise abstract in this paper we are concerned with almost automorphic solutions for semilinear stochastic differential equations driven by levy noise on the hilbert space we present a new variant of gronwall s lemma which improves the variant of gronwall s lemma in kamenskii 2015 based on this new variant of gronwall s lemma suitable conditions on the coefficients we prove the existence and uniqueness of almost automorphic solution in distribution for some stochastic differential equations driven by levy noise on the hilbert space which improves and generalizes the results in liu 2014 subsequently by using this new variant of gronwall s lemma we investigate the existence and uniqueness of almost automorphic solution in distribution for stochastic differential equations driven by levy noise with markov switching processes under some weaker conditions in the end two examples are given to illustrate the theoretical results obtained in this paper

numerical solutions for stochastic differential games with regime switching this paper is concerned with numerical methods for stochastic differential games of regime switching diffusions numerical methods using markov chain approximation techniques are developed a new proof of the existence of a saddle point for the stochastic differential game is provided this new proof enables us to treat certain systems with nonseparable in controls structure convergence of the algorithms is derived by means of weak convergence methods in addition examples are also provided for demonstration purposes

mean variance optimization of discrete time discounted markov decision processes abstract in this paper we study a mean variance optimization problem in an infinite horizon discrete time discounted markov decision process mdp the objective is to minimize the variance of system rewards with the constraint of mean performance different from most of works in the literature which require the mean performance already achieve optimum we can let the discounted performance equal any constant the difficulty of this problem is caused by the quadratic form of the variance function which makes the variance minimization problem not a standard mdp by proving the decomposable structure of the feasible policy space we transform this constrained variance minimization problem to an equivalent unconstrained mdp under a new discounted criterion and a new reward function the difference of the variances of markov chains under any two feasible policies is quantified by a difference formula based on the variance difference formula a policy iteration algorithm is developed to find the optimal policy we also prove the optimality of deterministic policy over the randomized policy generated in the mean constrained policy space numerical experiments demonstrate the effectiveness of our approach

markowitz s mean variance portfolio selection with regime switching a continuous time model a continuous time version of the markowitz mean variance portfolio selection model is proposed and analyzed for a market consisting of one bank account and multiple stocks the market parameters including the bank interest rate and the appreciation and volatility rates of the stocks depend on the market mode that switches among a finite number of states the random regime switching is assumed to be independent of the underlying brownian motion this essentially renders the underlying market incomplete a markov chain modulated diffusion formulation is employed to model the problem using techniques of stochastic linear quadratic control mean variance efficient portfolios and efficient frontiers are derived explicitly in closed forms based on solutions of two systems of linear ordinary differential equations related issues such as a minimum variance portfolio and a mutual fund theorem are also addressed all the results are markedly different from those for the case when there is no regime switching an interesting observation is however that if the interest rate is deterministic then the results exhibit rather unexpected similarity to their no regime switching counterparts even if the stock appreciation and volatility rates are markov modulated

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

valuation of stock loans with regime switching this paper is concerned with stock loan valuation in which the underlying stock price is dictated by geometric brownian motion with regime switching the stock loan pricing is quite different from that for standard american options because the associated variational inequalities may have infinitely many solutions in addition the optimal stopping time equals infinity with positive probability variational inequalities are used to establish values of stock loans and reasonable values of critical parameters such as loan sizes loan rates and service fees in terms of certain algebraic equations numerical examples are included to illustrate the results

integer multiplication with overflow detection or saturation high speed multiplication is frequently used in general purpose and application specific computer systems these systems often support integer multiplication where two n bit integers are multiplied to produce a 2n bit product to prevent growth in word length processors typically return the n least significant bits of the product and a flag that indicates whether or not overflow has occurred alternatively some processors saturate results that overflow to the most positive or most negative representable number this paper presents efficient methods for performing unsigned or two s complement integer multiplication with overflow detection or saturation these methods have significantly less area and delay than conventional methods for integer multiplication with overflow detection or saturation

two player zero sum stochastic differential games with regime switching abstract this paper is concerned with the two player zero sum stochastic differential game in a regime switching model with an infinite horizon the state of the system is characterized by a number of diffusions coupled by a continuous time finite state markov chain based on the dynamic programming principle dpp the lower and upper value functions are shown to be the unique viscosity solutions of the associated lower and upper hamilton jacobi bellman isaacs hjbi equations respectively moreover the lower and upper value functions coincide under the isaacs condition which implies that the game admits a value all the proofs in this paper are markedly different from those for the case when there is no regime switching

optimal control of the risk process in a regime switching environment this paper is concerned with cost optimization of an insurance company the surplus of the insurance company is modeled by a controlled regime switching diffusion in which the regime switching mechanism provides the fluctuations of the random environment the goal is to find an optimal control that minimizes the total cost up to a stochastic exit time a weaker sufficient condition than that of fleming and soner 2006 section v 2 for the continuity of the value function is obtained further the value function is shown to be a viscosity solution of a hamilton jacobi bellman equation

portfolio selection in a two regime world abstract standard mean variance analysis is based on the assumption of normal return distributions however a growing body of literature suggests that the market oscillates between two different regimes one with low volatility and the other with high volatility in such a case even if the return distributions are normal in both regimes the overall distribution is not it is a mixture of normals mean variance analysis is inappropriate in this framework and one must either assume a specific utility function or alternatively employ the more general and distribution free second degree stochastic dominance ssd criterion this paper develops the ssd rule for the case of mixed normals the ssdmn rule this rule is a generalization the mean variance rule the cost of ignoring regimes and assuming normality when the distributions are actually mixed normal can be quite substantial it is typically equivalent to an annual rate of return of 2 3 percent

an m ary detection approach for asset allocation abstract we develop a continuous time asset allocation model which incorporates both model uncertainty and structural changes in economic conditions a dynamic m ary detection framework for a continuous time hidden markov chain partially observed in a gaussian process is used to model the price dynamics of the risky asset and the hidden states of an economy the goal of an investor is to select an optimal asset portfolio mix so as to maximize the expected utility of terminal wealth filtering theory is used first to turn the problem into one with complete observations and then to derive m ary detection filters for the hidden system the hamilton jacobi bellman dynamic programming approach is used to solve the asset allocation problem with complete observations an explicit solution is obtained for the power utility case

portfolio selection with regime switching and state dependent preferences abstract in this paper we consider the consumption investment problem in a regime switching model with both the discount function and relative absolute risk aversion depending on the exogenous environment we obtain the solutions to this time inconsistent optimal control problem for both the sophisticated agent and the naive agent for different utilities we also give some comparisons between the strategies for these two kinds of agents our results show that at any time given the same wealth the naive agent with power resp exponential utility consumes less resp more than her his sophisticated counterpart in general and the sophisticated agent is more sensitive to the change of the exogenous environment

stock trading an optimal selling rule trading in stock markets consists of three major steps select a stock purchase a number of shares and eventually sell them to make a profit the timing to buy and sell is extremely crucial a selling rule can be specified by two preselected levels a target price and a stop loss limit this paper is concerned with an optimal selling rule based on the model characterized by a number of geometric brownian motions coupled by a finite state markov chain such a policy can be obtained by solving a set of two point boundary value differential equations moreover the corresponding expected target period and probability of making money and that of losing money are derived analytic solutions are obtained in one and two dimensional cases finally a numerical example is considered to demonstrate the effectiveness of our method

on optimal harvesting problems in random environments this paper investigates the optimal harvesting strategy for a single species living in random environments whose population growth is given by a regime switching diffusion harvesting acts as a stochastic control on the size of the population the objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to the time of extinction of the species the income rate is allowed to be state and environment dependent this is a singular stochastic control problem with both the extinction time and the optimal harvesting policy depending on the initial condition one aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy consequently one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon this paper introduces a new sufficient condition under which the continuity of the value function for the regime switching model is established further it is shown that the value function is a viscosity solution of a coupled system of quasi variational inequalities the paper also establishes a verification theorem and based on this theorem an varepsilon optimal harvesting strategy is constructed under certain conditions on the model two examples are analyzed in detail

maximum principle for optimal control problems of forward backward regime switching system and applications abstract in this paper we derive the stochastic maximum principle for optimal control problems of the forward backward markovian regime switching system the control system is described by forward backward sdes and modulated by continuous time finite state markov chains we first obtain the necessary and sufficient conditions for the optimal control thereafter we apply the maximum principle to recursive utility investment consumption problems and lq problems with markovian regime switching

optimal investment consumption strategy with liability and regime switching model under value at risk constraint abstract this paper considers the optimal investment consumption problem with liability subject to a maximum value at risk denoted by mvar constraint the model also contains regime switching market modes whose states are interpreted as the states of the economy in each state of economy state we constrain a var value for the portfolio in a short time duration and mvar is defined as the maximum value of the vars in all economy states we suppose that both the price dynamics of the risky asset and the liability value process are governed by a markov modulated geometric brownian motion with the objective of maximizing the discounted utility of consumption we obtain a system of hjb equations corresponding to the economy states by using the dynamic programming principle then by adopting the techniques of chen et al 2010 we get explicit expressions of value functions moreover with the help of lagrange multiplier method we derive the optimal investment and the optimal consumption finally a numerical example is investigated and the effects of many parameters on the optimal investment on the optimal consumption and on var value are studied furthermore we also explore how var value affects the optimal investment and the optimal consumption

mean variance portfolio selection under a non markovian regime switching model abstract in this paper we investigate the mean variance portfolio selection problem in a continuous time setting we assume that the coefficients in the model are random and adapted to the filtration generated by a markov chain instead of using the embedding approach which is widely adopted in the existing literature we study the problem from the viewpoint of mean field formulation and provide a distinctive and straightforward approach by introducing and discussing a new system of mean field backward stochastic differential equations driven by a markov chain we obtain both the optimal strategy and the efficient frontier in explicit forms in particular we revisit the markovian regime switching model in which the coefficients are deterministic functions of the markov chain

a generalized multi period mean variance portfolio optimization with markov switching parameters in this paper we deal with a generalized multi period mean variance portfolio selection problem with market parameters subject to markov random regime switchings problems of this kind have been recently considered in the literature for control over bankruptcy for cases in which there are no jumps in market parameters see zhu s s li d wang s y 2004 risk control over bankruptcy in dynamic portfolio selection a generalized mean variance formulation ieee transactions on automatic control 49 447 457 we present necessary and sufficient conditions for obtaining an optimal control policy for this markovian generalized multi period mean variance problem based on a set of interconnected riccati difference equations and on a set of other recursive equations some closed formulas are also derived for two special cases extending some previous results in the literature we apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with markov jumps selection problem

recursive algorithms for stock liquidation a stochastic optimization approach this work develops stochastic optimization algorithms for a class of stock liquidation problems the stock liquidation rules are based on hybrid geometric brownian motion models allowing regime changes that are modulated by a continuous time finite state markov chain the optimal selling policy is of threshold type and can be obtained by solving a set of two point boundary value problems the total number of equations to be solved is the same as the number of states of the underlying markov chain to reduce the computational burden using a stochastic optimization approach recursive algorithms are constructed to approximate the optimal threshold values convergence and rates of convergence of the algorithm are studied simulation examples are presented and the computation results are compared with the analytic solutions finally the algorithms are tested using real market data

properties of the solutions of the linearized monge ampere equation let r n r be a function strictly convex and smooth and det d 2 is the monge ampere generated by given x r n and t 0 let s x t y r n y x x y x t the purpose of this paper is to study the properties of the solutions of the linearized monge ampere equation given by a ij x d ij u 0 where the coefficients a ij x are the cofactors of the matrix d 2 x it is assumed that satisfies a doubling condition on the sets s x t and a uniform continuity condition at every scale with respect to lebesgue measure we establish that the distribution functions of nonnegative solutions u at altitude t decay like a negative power of t and prove an invariant harnack s inequality on the sections s x t all the estimates are independent of the regularity of and depend only on the constants in the hypotheses made on the measure

a new design technique for column compression multipliers in this paper a new design technique for column compression cc multipliers is presented constraints for column compression with full and half adders are analyzed and under these constraints considerable flexibility for implementation of the cc multiplier including the allocation of adders and choosing the length of the final fast adder is exploited using the example of an 8 spl times 8 bit cc multiplier we show that architectures obtained from this new design technique are more area efficient and have shorter interconnections than the classical dadda cc multiplier we finally show that our new technique is also suitable for the design of twos complement multipliers

dual method for continuous time markowitz s problems with nonlinear wealth equations continuous time mean variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method a necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique it is also shown that the optimal wealth and portfolio is the solution of a forward backward stochastic differential equation with constraints

numerical solutions of quantile hedging for guaranteed minimum death benefits under a regime switching jump diffusion formulation this work develops numerical approximation methods for quantile hedging involving mortality components for contingent claims in incomplete markets in which guaranteed minimum death benefits gmdbs could not be perfectly hedged a regime switching jump diffusion model is used to delineate the dynamic system and the hedging function for gmdbs where the switching is represented by a continuous time markov chain using markov chain approximation techniques a discrete time controlled markov chain with two component is constructed under simple conditions the convergence of the approximation to the value function is established examples of quantile hedging model for guaranteed minimum death benefits under linear jumps and general jumps are also presented

covering theorems inequalities on metric spaces and applications to pde s we establish a covering lemma of besicovitch type for metric balls in the setting of holder quasimetric spaces of homogenous type and use it to prove a covering theorem for measurable sets for families of measurable functions we introduce the notions of power decay critical density and double ball property and with the aid of the covering theorem we show how these notions are related next we present an axiomatic procedure to establish harnack inequality that permits to handle both divergence and non divergence linear equations

superreplication under gamma constraints in a financial market consisting of a nonrisky asset and a risky one we study the minimal initial capital needed in order to superreplicate a given contingent claim under a gamma constraint this is a constraint on the unbounded variation part of the hedging portfolio we first consider the case in which the prices are given as general markov diffusion processes and prove a verification theorem which characterizes the superreplication cost as the unique solution of a quasi variational inequality in the context of the black scholes model i e when volatility is constant this theorem allows us to derive an explicit solution of the problem these results are based on a new dynamic programming principle for general stochastic target problems

spectral method for analysis of switching diffusions the analysis problem of switching diffusions is considered this paper presents a new approach based on the spectral method formalism for solving generalized fokker planck equations the proposed method allows to transform partial differential equations into the linear algebraic equations and to arrive at a solution in an explicit form the aspects of applications are discussed a numerical example is given to illustrate the efficiency of the proposed method

approximation pricing and the variance optimal martingale measure let x be a semimartingale and let be the space of all predictable x integrable processes v such that so dx is in the space s 2 of semi martingales we consider the problem of approximating a given random variable h l 2 p by the sum of a constant c and a stochastic integral s 0 t v s dx s with respect to the l 2 p norm this problem comes from financial mathematics where the optimal constant v 0 can be interpreted as an approximation price for the contingent claim h an elementary computation yields v 0 as the expectation of h under the variance optimal signed martingale measure p and this leads us to study p in more detail in the case of finite discrete time we explicitly construct p by backward recursion and we show that p is typically not a probability but only a signed measure in a continuous time framework the situation becomes rather different we prove that p is nonnegative if x has continuous paths and satisfies a very mild no arbitrage condition as an application we show how to obtain the optimal integrand in feedback form with the help of a backward stochastic differential equation

uncertain exit time multi period mean variance portfolio selection with endogenous liabilities and markov jumps this paper considers an uncertain exit time multi period mean variance portfolio selection problem with endogenous liabilities in a markov jump market where assets and liabilities of the balance sheet are simultaneously optimized the random returns of assets and liabilities depend on the states of the financial market by applying the lagrange duality method the khatri rao matrix product technique and the dynamic programming approach the explicit expressions for the mean variance efficient strategy and efficient frontier are derived in addition the optimal balance sheet structures in both cases with and without boundary constraints are studied moreover some degenerate cases are discussed and some results in the literature are recovered as degenerate cases under our setting furthermore a numerical example based on real data from the chinese stock market is provided to illustrate the results obtained in this paper and some interesting findings are presented

markowitz s mean variance portfolio selection with regime switching from discrete time models to their continuous time limits we study a discrete time version of markowitz s mean variance portfolio selection problem where the market parameters depend on the market mode regime that jumps among a finite number of states the random regime switching is delineated by a finite state markov chain based on which a discrete time markov modulated portfolio selection model is presented such models either arise from multiperiod portfolio selections or result from numerical solution of continuous time problems the natural connections between discrete time models and their continuous time counterpart are revealed since the markov chain frequently has a large state space to reduce the complexity an aggregated process with smaller state space is introduced and the underlying portfolio selection is formulated as a two time scale problem we prove that the process of interest yields a switching diffusion limit using weak convergence methods next based on the optimal control of the limit process obtained from our recent work we devise portfolio selection strategies for the original problem and demonstrate their asymptotic optimality

harnack inequality for a subelliptic pde in nondivergence form abstract we consider subelliptic equations in non divergence form of the type l u i j a i j x j x i u 0 where x j are the grushin vector fields and the matrix coefficient is uniformly elliptic we obtain a scale invariant harnack s inequality on the x j s cc balls for nonnegative solutions under the only assumption that the ratio between the maximum and minimum eigenvalues of the coefficient matrix is bounded in the paper we first prove a weighted aleksandrov bakelman pucci estimate and then we show a critical density estimate the double ball property and the power decay property once this is established harnack s inequality follows directly from the axiomatic theory developed by di fazio gutierrez and lanconelli in di fazio et al 2008

a mean variance optimization problem for discounted markov decision processes in this paper we consider a mean variance optimization problem for markov decision processes mdps over the set of deterministic stationary policies different from the usual formulation in mdps we aim to obtain the mean variance optimal policy that minimizes the variance over a set of all policies with a given expected reward for continuous time mdps with the discounted criterion and finite state and action spaces we prove that the mean variance optimization problem can be transformed to an equivalent discounted optimization problem using the conditional expectation and markov properties then we show that a mean variance optimal policy and the efficient frontier can be obtained by policy iteration methods with a finite number of iterations we also address related issues such as a mutual fund theorem and illustrate our results with an example

near optimal controls of random switching lq problems with indefinite control weight costs in this paper we consider hybrid controls for a class of linear quadratic problems with white noise perturbation and markov regime switching where the regime switching is modeled by a continuous time markov chain with a large state space and the control weights are indefinite the use of large state space enables us to take various factors of uncertain environment into consideration yet it creates computational overhead and adds difficulties aiming at reduction of complexity we demonstrate how to construct near optimal controls first in the model we introduce a small parameter to highlight the contrast of the weak and strong interactions and fast and slow motions this results in a two time scale formulation in view of the recent developments on lq problems with indefinite control weights and two time scale markov chains we then establish the convergence of the system of riccati equations associated with the hybrid lq problem based on the optimal feedback control of the limit system obtained using the system of riccati equations we construct controls for the original problem and show that such controls are near optimal a numerical demonstration of a simple system is presented here

some new liouville type results for fully nonlinear pdes on the heisenberg group abstract we prove new sharp liouville type properties via degenerate hadamard three sphere theorems for fully nonlinear equations structured over heisenberg vector fields as model examples we cover the case of pucci s extremal operators perturbed by suitable semilinear and gradient terms extending to the heisenberg setting known contributions valid in the euclidean framework

optimal portfolio selection with liability management and markov switching under constrained variance in this paper we mainly discuss an optimal portfolio selection model with liability management and markov switching which maximize the expected final surplus under constrained variance because linear quadratic control is a basic method for the m v problem in this paper we begin with the general stochastic linear quadratic model and obtain the optimal solution of the problem exactly the analytical optimal portfolio strategy is derived in this paper furthermore we demonstrate that a special case is consistent with those results of chiu and li 2006 3

a generalized multibit recoding of two s complement binary numbers and its proof with application in multiplier implementations a multibit recoding algorithm for signed two s complement binary numbers is presented and proved in general a k 1 bit recoding will result in a signed digit sd representation of the binary number in radix 2 sup k using digits 2 sup k 1 to 2 sup k 1 including 0 it is shown that a correct sd representation of the original number is obtained by scanning k 1 tuples k or 1 with one bit overlapping between adjacent groups recording of binary numbers has been used in computer arithmetic with 3 bit recoding being the dominant scheme with the emergence of very high speed adders hardware parallel multipliers using multibit recoding with k 2 are feasible with the potential of improving both the performance and the hardware requirements a parallel hardware multiplier based on the specific case of 5 bit recoding is proposed extensions beyond 5 bit recoding for multiplier design are studied for their performance and hardware requirements other issues relating to multiplier design such as multiplication by a fixed or controlled coefficient are also discussed in the light of multibit recoding

discrete time mean variance optimal control of linear systems with markovian jumps and multiplicative noise in this article we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output in the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system we present explicit sufficient conditions for the existence of an optimal control strategy for these problems generalising previous results in the literature we conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching

polar coordinates in carnot groups we describe a procedure for constructing polar coordinates in a certain class of carnot groups we show that our construction can be carried out in groups of heisenberg type and we give explicit formulas for the polar coordinate decomposition in that setting the construction makes use of nonlinear potential theory specifically fundamental solutions for the p sub laplace operators as applications of this result we obtain exact capacity estimates representation formulas and an explicit sharp constant for the moser trudinger inequality we also obtain topological and measure theoretic consequences for quasiregular mappings

portfolio selection in the enlarged markovian regime switching market we study a portfolio selection problem in a continuous time markovian regime switching model the market in this model is in general incomplete we adopt a method to complete the market based on an enlargement of the market using a set of geometric markovian jump securities we solve the portfolio selection problem in the enlarged market for a power utility and a logarithmic utility closed form solutions for the optimal portfolio strategies and the value functions are obtained in both cases we also establish the relationship between the optimal portfolio problems in the enlarged market and the original market

a lattice based approach to option and bond valuation under mean reverting regime switching diffusion processes abstract nowadays the pricing of financial instruments under continuous time markov switching models have received a widespread attention from researchers and practitioners in the finance industry lattice based approaches are amongst the most widely used approaches to solve the pricing problem in this context recently yuen and yang 2010 have proposed a simple and fast recombining trinomial tree method to handle the case of regime switching geometric brownian motion processes in this paper we generalize their approach to the regime switching exponential mean reverting case with state dependent switching rates and derive the necessary conditions for the positivity of conditional branching probabilities we employ the hull and white s tree building procedure to limit tree growth away from the long run mean of the process we use the proposed lattice framework to price contingent claims of european american and barrier type and demonstrate its applicability in pricing default free zero coupon bonds in the proposed tree structure the number of nodes is substantially decreased and the computational cost is effectively reduced compared to the usual approaches extensive numerical experiments illustrate the efficiency and flexibility of the proposed scheme

a certain critical density property for invariant harnack inequalities in h type groups abstract we consider second order linear degenerate elliptic operators which are elliptic with respect to horizontal directions generating a stratified algebra of h type extending a result by gutierrez and tournier 2011 for the heisenberg group we prove a critical density estimate by assuming a condition of cordes landis type we then deduce an invariant harnack inequality for the non negative solutions from a result by di fazio gutierrez and lanconelli 2008

relationship between backward stochastic differential equations and stochastic controls a linear quadratic approach it is well known that backward stochastic differential equations bsdes stem from the study on the pontryagin type maximum principle for optimal stochastic controls a solution of a bsde hits a given terminal value which is a random variable by virtue of an it additional martingale term and an indefinite initial state this paper attempts to explore the relationship between bsdes and stochastic controls by interpreting bsdes as some stochastic optimal control problems more specifically associated with a bsde a new stochastic control problem is introduced with the same dynamics but a definite given initial state the martingale term in the original bsde is regarded as the control and the objective is to minimize the second moment of the difference between the terminal state and the terminal value given in the bsde this problem is solved in a closed form by the stochastic linear quadratic lq theory developed recently the general result is then applied to the black scholes model where an optimal mean variance hedging portfolio is obtained explicitly in terms of the option price finally a modified model is investigated where the difference between the state and the expectation of the given terminal value at any time is taken into account

optimal portfolios with regime switching and value at risk constraint we consider the optimal portfolio selection problem subject to a maximum value at risk mvar constraint when the price dynamics of the risky asset are governed by a markov modulated geometric brownian motion gbm here the market parameters including the market interest rate of a bank account the appreciation rate and the volatility of the risky asset switch over time according to a continuous time markov chain whose states are interpreted as the states of an economy the mvar is defined as the maximum value of the vars of the portfolio in a short time duration over different states of the chain we formulate the problem as a constrained utility maximization problem over a finite time horizon by utilizing the dynamic programming principle we shall first derive a regime switching hamilton jacobi bellman hjb equation and then a system of coupled hjb equations we shall employ an efficient numerical method to solve the system of coupled hjb equations for the optimal constrained portfolio we shall provide numerical results for the sensitivity analysis of the optimal portfolio the optimal consumption and the var level with respect to model parameters these results are also used to investigating the effect of the switching regimes

optimal mean variance control for discrete time linear systems with markovian jumps and multiplicative noises in this paper we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noises under two criteria the first one is an unconstrained mean variance trade off performance criterion along the time and the second one is a minimum variance criterion along the time with constraints on the expected output we present explicit conditions for the existence of an optimal control strategy for the problems generalizing previous results in the literature we conclude the paper by presenting a numerical example of a multi period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor

almost sure stabilization for feedback controls of regime switching linear systems with a hidden markov chain this work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown markov chain the control system displays continuous dynamics represented by differential equations and discrete events given by a hidden markov chain in the previous investigation on this class of problems averaging criteria were used which provides only the system behavior in some expectation sense a closer scrutiny of the system behavior necessarily requires the consideration of sample path properties different from previous work on stabilization of adaptive controlled systems with a hidden markov chain where average criteria were considered this work focuses on the almost sure stabilization or sample path stabilization of the underlying processes under simple conditions it is shown that as long as the feedback controls have linear growth in the continuous component the resulting process is regular moreover by appropriate choice of the lyapunov functions it is shown that the adaptive system is stabilizable almost surely as a by product it is also established that the controlled process is positive recurrent

abstract approach to non homogeneous harnack inequality in doubling quasi metric spaces abstract we develop an abstract theory to obtain harnack inequality for non homogeneous pdes in the setting of quasi metric spaces the main idea is to adapt the notion of double ball and critical density property given by di fazio gutierrez lanconelli taking into account the right hand side of the equation then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving grushin vector fields and to the case of x elliptic operators in divergence form

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

multiplexer based array multipliers a new algorithm for the multiplication of two n bit numbers based on the synchronous computation of the partial sums of the two operands is presented the proposed algorithm permits an efficient realization of the parallel multiplication using iterative arrays at the same time it permits high speed operation multiplier arrays for positive numbers and numbers in two s complement form based on the proposed technique are implemented also an efficient pipeline form of the proposed multiplication scheme is introduced all multipliers obtained have low circuit complexity permitting high speed operation and the interconnections of the cells are regular well suited for vlsi realization

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

harnack inequality for a class of kolmogorov fokker planck equations in non divergence form we prove invariant harnack inequalities for certain classes of non divergence form equations of kolmogorov type the operators we consider exhibit invariance properties with respect to a homogeneous lie group structure the coefficient matrix is assumed either to satisfy a cordes landis condition on the eigenvalues or to admit a uniform modulus of continuity

a lattice method for option pricing with two underlying assets in the regime switching model abstract in this work we develop an efficient lattice approach for option pricing with two underlying assets whose prices are governed by regime switching models jump amplitudes are specified in a way such that the lattice achieves complete node recombination along each asset variable and grows quadratically as the number of time steps increases jump probabilities are obtained by solving a related quadratic programming problem the weak convergence of the discrete lattice approximations to the continuous time regime switching diffusion processes is established the lattice is employed to price both european and american options written on the maximum and minimum of two assets in different regimes numerical results are provided and compared for the european options with a monte carlo simulation approach

robust m ary detection filters and smoothers for continuous time jump markov systems in this paper we consider a dynamic m ary detection problem when markov chains are observed through a wiener process these systems are fully specified by a candidate set of parameters whose elements are a rate matrix for the markov chain and a parameter for the observation model further we suppose these parameter sets can switch according to the state of an unobserved markov chain and thereby produce an observation process generated by time varying jump stochastic parameter sets given such an observation process and a specified collection of models we estimate the probabilities of each model parameter set explaining the observation by defining a new augmented state process then applying the method of reference probability we compute matrix valued dynamics whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process these matrix valued dynamics satisfy a stochastic integral equation with a wiener process integrator using the gauge transformation techniques introduced by clark and a pointwise matrix product we compute robust matrix valued dynamics for the joint probabilities on the augmented state space in these new dynamics the observation wiener process appears as a parameter matrix in a linear ordinary differential equation rather than an integrator in a stochastic integral equation it is shown that these robust dynamics when discretised enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path in contrast no such upper bounds can be computed for taylor expansion approximations such as the euler maryauana and milstein schemes finally by exploiting a duality between causal and anticausal robust detector dynamics we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations a computer simulation demonstrating performance is included

upper and lower solutions for regime switching diffusions with applications in financial mathematics this paper develops a method of upper and lower solutions for a general system of second order ordinary differential equations with two point boundary conditions our motivation of study stems from a class of financial mathematics problems under regime switching diffusion models two examples are double barrier option valuation and optimal selling rules in asset trading we establish the existence of a unique c 2 solution of the two point boundary value problem we construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem this construction provides a feasible numerical method to compute approximate solutions an important feature of the proposed numerical method is that the unique solution is bracketed by the upper and lower approximate solutions which provide an interval estimate of the unique solution function we apply the general results to a regime switching mean reverting model and improve related results already rep

a stochastic maximum principle for a markov regime switching jump diffusion model and its application to finance this paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem where the state process is governed by a continuous time markov regime switching jump diffusion model we also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a markovian case applications of the stochastic maximum principle to the mean variance portfolio selection problem are discussed

numerical methods for portfolio selection with bounded constraints this work develops an approximation procedure for portfolio selection with bounded constraints based on the markov chain approximation techniques numerical procedures are constructed for the utility optimization task under simple conditions the convergence of the approximation sequences to the wealth process and the optimal utility function is established numerical examples are provided to illustrate the performance of the algorithms