on singular control problems with state constraints and regime switching this paper investigates a singular stochastic control problem for a multi dimensional regime switching diffusion process confined in an unbounded domain the objective is to maximize the total expected discounted rewards from exerting the singular control such a formulation stems from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in random environments with the aid of weak dynamic programming principle and an exponential transformation we characterize the value function to be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi variational inequalities several examples are analyzed in detail to demonstrate the main results

on weak solutions of forward backward sdes in this paper we continue exploring the notion of weak solution of forward backward stochastic differential equations fbsdes and associated forward backward martingale problems fbmps the main purpose of this work is to remove the constraints on the martingale integrands in the uniqueness proofs in our previous work ma et al in ann probab 36 6 2092 2125 2008 we consider a general class of non degenerate fbsdes in which all the coefficients are assumed to be essentially only bounded and uniformly continuous and the uniqueness is proved in the space of all the square integrable adapted solutions the standard solution space in the fbsde literature a new notion of semi strong solution is introduced to clarify the relations among different definitions of weak solution in the literature and it is in fact instrumental in our uniqueness proof as a by product we also establish some a priori estimates of the second derivatives of the solution to the decoupling quasilinear pde

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

weak dynamic programming principle for viscosity solutions we prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control stopping problems which avoids the technical difficulties related to the measurable selection argument in the markov case our result is tailor made for the derivation of the dynamic programming equation in the sense of viscosity solutions

a weak dynamic programming principle for combined optimal stopping stochastic control with cal e f expectations we study a combined optimal control stopping problem under a nonlinear expectation e f induced by a bsde with jumps in a markovian framework the terminal reward function is only supposed to be borelian the value function u associated with this problem is generally irregular we first establish a sub resp super optimality principle of dynamic programming involving its upper resp lower semicontinuous envelope u resp u this result called the weak dynamic programming principle dpp extends that obtained in bouchard and touzi siam j control optim 49 2011 pp 948 962 in the case of a classical expectation to the case of an e f expectation and borelian terminal reward function using this weak dpp we then prove that u resp u is a viscosity sub resp super solution of a nonlinear hamilton jacobi bellman variational inequality

maximizing expected terminal utility of an insurer with high gain tax by investment and reinsurance abstract this paper investigates optimal investment and proportional reinsurance policies for an insurer who subjects to pay high gain tax the surplus process of the insurer and the return process of the financial market are both modulated by the external macroeconomic environment the dynamic of the external macroeconomic environment is specified by a markov chain with finite states once the insurer s accumulated profits attain a new maximum they have to pay high gain tax the objective of the insurer is to maximize the expected terminal utility by investment and reinsurance the controlled wealth process of the insurer turned out to be a controlled jump diffusion process with reflections and markov regime switching by the weak dynamic programming principle wdpp we prove that the value function is the unique viscosity solution to the coupled hamilton jacob bellman hjb equations with first derivative boundary constraints by the markov chain approximating method for the hjb equations we construct a numerical scheme for approximating the viscosity solution to the coupled hjb equations two numerical examples are presented to illustrate the impact of both high gain tax and regime switching on the optimal policies

on 3 extra connectivity and 3 extra edge connectivity of folded hypercubes given a graph mbi g and a non negative integer g the g extra connectivity resp g extra edge connectivity of mbi g is the minimum cardinality of a set of vertices resp edges in mbi g if it exists whose deletion disconnects mbi g and leaves each remaining component with more than g vertices this study shows that the 3 extra connectivity resp 3 extra edge connectivity of an mbi n dimensional folded hypercube is 4 n 5 for n geq 6 resp 4 n 4 for n geq 5 this study also provides an upper bound for the g extra connectivity on folded hypercubes for g geq 6

on the multidimensional controller and stopper games we consider a zero sum stochastic differential controller and stopper game in which the state process is a controlled diffusion evolving in a multidimensional euclidean space in this game the controller affects both the drift and diffusion terms of the state process and the diffusion term can be degenerate under appropriate conditions we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a hamilton jacobi bellman equation

on the lp formulation in measure spaces of optimal control problems for jump diffusions abstract in this short note we formulate a infinite horizon stochastic optimal control problem for jump diffusions of ito levy type as a lp problem in a measure space and prove that the optimal value functions of both problems coincide the main tools are the dual formulation of the lp primal problem which is strongly connected to the notion of sub solution of the partial integro differential equation of hamilton jacobi bellman type associated with the optimal control problem and the krylov regularization method for viscosity solutions

an lp approach to dynamic programming principles for stochastic control problems with state constraints abstract we study a class of nonlinear stochastic control problems with semicontinuous cost and state constraints using a linear programming lp approach first we provide a primal linearized problem stated on an appropriate space of probability measures with support contained in the set of constraints this space is completely characterized by the coefficients of the control system second we prove a semigroup property for this set of probability measures appearing in the definition of the primal value function this leads to dynamic programming principles for control problems under state constraints with general bounded costs a further linearized dpp is obtained for lower semicontinuous costs

the stochastic reach avoid problem and set characterization for diffusions in this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective preceding approaches to solving these reachability problems are either confined to the deterministic setting or address almost sure stochastic requirements in contrast we propose a methodology to tackle problems with less stringent requirements than almost sure to this end we first establish a connection between two distinct stochastic reach avoid problems and three classes of stochastic optimal control problems involving discontinuous payoff functions subsequently we focus on solutions of one of the classes of stochastic optimal control problems the exit time problem which solves both the two reach avoid problems mentioned above we then derive a weak version of a dynamic programming principle dpp for the corresponding value function in this direction our contribution compared to the existing literature is to develop techniques that admit discontinuous payoff functions moreover based on our dpp we provide an alternative characterization of the value function as a solution of a partial differential equation pde in the sense of discontinuous viscosity solutions along with boundary conditions both in dirichlet and viscosity senses theoretical justifications are also discussed to pave the way for deployment of off the shelf pde solvers for numerical computations finally we validate the performance of the proposed framework on the stochastic zermelo navigation problem

characterization of the optimal boundaries in reversible investment problems this paper studies a reversible investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good our model allows for general diffusion dynamics on the demand as well as general cost functional the resulting optimization problem leads to a degenerate two dimensional bounded variation singular stochastic control problem for which explicit solution is not available in general and the standard verification approach cannot be applied a priori we use a direct viscosity solutions approach for deriving some features of the optimal free boundary function and for displaying the structure of the solution in the quadratic cost case we are able to prove a smooth fit c 2 property which gives rise to a full characterization of the optimal boundaries and value function

structure fault tolerance of hypercubes and folded hypercubes abstract let g be a graph and t be a certain connected subgraph of g the t structure connectivity g t resp t substructure connectivity s g t of g is the minimum number of a set of subgraphs f t 1 t 2 t m resp f t 1 t 2 t m such that t i is isomorphic to t resp t i is a connected subgraph of t for every 1 i m and f s removal will disconnect g let q n and f q n denote the n dimensional hypercube and folded hypercube respectively in 12 the q n t and s q n t were determined for t k 1 1 k 1 2 k 1 3 c 4 in this paper we generalize the above results by determining q n t and s q n t for t p k c 2 k k 1 4 where 3 k n we also determine f q n t and s f q n t for t p k c 2 k k 1 3 where n 7 and 2 k n

fault free hamiltonian cycles in crossed cubes with conditional link faults the crossed cube which is a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each node is incident with at least two fault free links we show that an n dimensional crossed cube contains a fault free hamiltonian cycle even if there are up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated we also verify that the assumption is practically meaningful by evaluating its occurrence probability which is very close to 1

optimal switching with constraints and utility maximization of an indivisible market this work focuses on optimal switching with constraints our motivation stems from utility maximization of an indivisible market the dynamic programming approach is used the value function is characterized as the unique viscosity solution of a quasi variational inequality the unbounded domain introduces new challenges by studying the sample paths of the diffusion at the boundary a sufficient condition for the continuity of the value function is provided yielding the desired characterization not only are the results of this work applicable to the utility maximization problem but also they can be used for general optimal switching problems with finite regimes

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

optimal exploitation of a resource with stochastic population dynamics and delayed renewal in this work we study the optimization problem of a renewable resource in finite time the resource is assumed to evolve according to a logistic stochastic differential equation the manager may harvest partially the resource at any time and sell it at a stochastic market price she may equally decide to renew part of the resource but uniquely at deterministic times however we realistically assume that there is a delay in the renewing order by using the dynamic programming theory we may obtain the pde characterization of our value function to complete our study we give an algorithm to compute the value function and optimal strategy some numerical illustrations will be equally provided

optimal investment decision under switching regimes of subsidy support abstract we address the problem of making a managerial decision when the investment project is subsidized which results in the resolution of an infinite horizon optimal stopping problem of a switching diffusion driven by either a homogeneous or an inhomogeneous continuous time markov chain we provide a characterization of the value function and optimal strategy of the optimal stopping problem on the one hand broadly we can prove that the value function is the unique viscosity solution to a system of hjb equations on the other hand when the markov chain is homogeneous and the switching diffusion is one dimensional we obtain stronger results the value function is the difference between two convex functions

on reliability of the folded hypercubes in this paper we explore the 2 extra connectivity and 2 extra edge connectivity of the folded hypercube fq n we show that k 2 fq n 3n 2 for n 8 and l 2 fq n 3n 1 for n 5 that is for n 8 resp n 5 at least 3n 2 vertices resp 3n 1 edges of fq n are removed to get a disconnected graph that contains no isolated vertices resp edges when the folded hypercube is used to model the topological structure of a large scale parallel processing system these results can provide more accurate measurements for reliability and fault tolerance of the system

infinite horizon stochastic optimal control problems with running maximum cost an infinite horizon stochastic optimal control problem with running maximum cost is considered the value function is characterized as the viscosity solution of a second order hjb equation with mixed boundary condition a general numerical scheme is proposed and convergence is established under the assumptions of consistency monotonicity and stability of the scheme a convergent semi lagrangian scheme is presented in detail

ols or gls in the presence of specification error an expected loss approach omitted variables in regression analysis can lead to the erroneous conclusion that autocorrelation or heteroscedasticity is present the common response is to use the suggested gls procedure even if it is suspected that the error is a non zero disturbance mean the question addressed here is whether one is better off with the gls or with the ols estimator when the omitted portion of the regression cannot be incorporated into the regression using a loss function this paper relates the seriousness of ols and gls loss to identifiable parameters with consistent estimators of these parameters the researcher can choose between ols and gls

reliability measures in relation to the h extra edge connectivity of folded hypercubes the folded hypercube fq n as a variation of the hypercube q n was proposed by a el amawy and s latifi in 1991 the h extra edge connectivity of the underlying topological graph of a multiprocessor system is a kind of measure for the reliability of the multiprocessor system in this paper we determine the exact value of h fq n for integer h 1 h 2 n 2 1 and 6 n which generalizes several known results for h n more interestingly we also show that h fq n is the constant n 2 r 1 2 n 2 r for 2 n 2 r l r h 2 n 2 r where r 1 2 n 2 1 and l r 2 2 r 1 3 if n is odd and l r 2 2 r 1 2 3 if n is even in particular for r n 2 1 2 n 2 3 h 2 n 1 h fq n 2 n

reliability analysis of bijective connection networks in terms of the extra edge connectivity reliability evaluation of interconnection network is of significant importance to the design and maintenance of multiprocessor systems the extra edge connectivity also called restricted edge connectivity is an important parameter for the reliability evaluation of interconnection network in this paper we find a method to study the h extra edge connectivity of an n dimensional bijective connection network in brief bc network also called hypercube like network as an application we determine h extra edge connectivity of an n dimensional bc network is a constant 2n 1 for 2n 1 2f3 h 2n 1 n 4 where f 0 when n is even and f 1 when n is odd we also show that the lower bound of h is sharp this paper also obtains the exact value of h extra edge connectivity of an n dimensional bc network for 1 h 2 n2 1 n 4 besides since the bc network includes several well known network models such as hypercubes twisted cubes crossed cubes mobius cubes locally twisted cubes generalized twisted cubes and mcubes so the previous results on the h extra edge connectivity of these networks are our corollaries

the three pass regression filter a new approach to forecasting using many predictors we forecast a single time series using many predictor variables with a new estimator called the three pass regression lter 3prf it is calculated in closed form and conveniently represented as a set of ordinary least squares regressions 3prf forecasts converge to the infeasible best forecast when both the time dimension and cross section dimension become large this requires only specifying the number of relevant factors driving the forecast target regardless of the total number of common including potentially irrelevant factors driving the cross section of predictors we derive inferential theory including limiting distributions for estimated relevant factors predictive coefcients and forecasts and provide consistent standard error estimators we explore two empirical applications forecasting macroeconomic aggregates with a large panel of economic indices and forecasting stock market aggregates with many individual assets price dividend ratios these combined with a range of monte carlo experiments demonstrate the 3prf s forecasting power

on the uniqueness of unbounded viscosity solutions arising in an optimal terminal wealth problem with transaction costs we study the uniqueness of viscosity solutions of a hamilton jacobi bellman equation which arises in a portfolio optimization problem in which an investor maximizes expected utility of terminal wealth in the presence of proportional transaction costs our main contribution is that the comparison theorem can be applied to prove the uniqueness of the value function in the portfolio optimization problem for logarithmic and power utility

a weak dynamic programming principle for zero sum stochastic differential games with unbounded controls we analyze a zero sum stochastic differential game between two competing players who can choose unbounded controls the payoffs of the game are defined through backward stochastic differential equations we prove that each player s priority value satisfies a weak dynamic programming principle and thus solves the associated fully nonlinear partial differential equation in the viscosity sense

edge fault tolerance analysis of a class of interconnection networks fault tolerant measures have played an important role in the reliability of an interconnection network edge connectivity restricted edge connectivity extra edge connectivity and super edge connectivity of many well known interconnection networks have been explored in this paper we study the 2 extra edge connectivity of a special class of graphs g g0 g1 m proposed by chen et al appl math comput 140 2003 245 254 then by showing that several well known interconnection networks such as hyper

weak dynamic programming for generalized state constraints we provide a dynamic programming principle for stochastic optimal control problems with expectation constraints a weak formulation using test functions and a probabilistic relaxation of the constraint avoids restrictions related to a measurable selection but still implies the hamilton jacobi bellman equation in the viscosity sense we treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints

wellposedness of second order backward sdes we provide an existence and uniqueness theory for an extension of backward sdes to the second order while standard backward sdes are naturally connected to semilinear pdes our second order extension is connected to fully nonlinear pdes as suggested in cheridito et al commun pure appl math 60 7 1081 1110 2007 in particular we provide a fully nonlinear extension of the feynman kac formula unlike cheridito et al in commun pure appl math 60 7 1081 1110 2007 the alternative formulation of this paper insists that the equation must hold under a non dominated family of mutually singular probability measures the key argument is a stochastic representation suggested by the optimal control interpretation and analyzed in the accompanying paper soner et al in dual formulation of second order target problems arxiv 1003 6050 2009

impulse control of multidimensional jump diffusions in finite time horizon this paper analyzes a class of impulse control problems for multidimensional jump diffusions in the finite time horizon following the basic mathematical setup from stroock and varadhan multidimensional diffusion processes springer verlag heidelberg 2006 this paper first establishes rigorously an appropriate form of the dynamic programming principle it then shows that the value function is a viscosity solution for the associated hamilton jacobi bellman equation involving integro differential operators finally under additional assumptions that the jumps are of infinite activity but are of finite variation and that the diffusion is uniformly elliptic it proves that the value function is the unique viscosity solution and has w loc 2 1 p regularity for 1 p infty

stochastic control for a class of nonlinear kernels and applications we consider a stochastic control problem for a class of nonlinear kernels more precisely our problem of interest consists in the optimization over a set of possibly non dominated probability measures of solutions of backward stochastic differential equations bsdes since bsdes are non linear generalizations of the traditional linear expectations this problem can be understood as stochastic control of a family of nonlinear expectations or equivalently of nonlinear kernels our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting which we then use to provide a semimartingale characterization of the value function we next explore several applications of our results we first obtain a wellposedness result for second order bsdes as introduced in 76 which does not require any regularity assumption on the terminal condition and the generator then we prove a non linear optional decomposition in a robust setting extending recent results of 63 which we then use to obtain a superhedging duality in uncertain incomplete and non linear financial markets finally we relate under additional regularity assumptions the value function to a viscosity solution of an appropriate path dependent partial differential equation ppde

generalized least squares with misspecified serial correlation structures summary the regression literature contains hundreds of studies on serially correlated disturbances most of these studies assume that the structure of the error covariance matrix q is known or can be estimated consistently from data surprisingly few studies investigate the properties of estimated generalized least squares gls procedures when the structure of q is incorrectly identified and the parameters are inefficiently estimated we compare the finite sample efficiencies of ordinary least squares ols gls and incorrect gls igls estimators we also prove new theorems establishing theoretical efficiency bounds for igls relative to gls and ols results from an exhaustive simulation study are used to evaluate the finite sample performance and to demonstrate the robustness of igls estimates vis a vis ols and gls estimates constructed for models with known and estimated but correctly identified q some of our conclusions for finite samples differ from established asymptotic results

optimal control versus stochastic target problems an equivalence result abstract within a general abstract framework we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in soner and touzi 2002 5 whenever the underlying filtered probability space admits a suitable martingale representation property this provides a unified way of treating these two classes of stochastic control problems as an illustration we show within a jump diffusion framework how the hamilton jacobi bellman equations associated to an optimal control problem in standard form can be easily retrieved from the partial differential equations associated to its stochastic target counterpart

on g extra conditional diagnosability of hypercubes and folded hypercubes abstract diagnosability of a multiprocessor system is one important study topic which plays an important role in measuring of the reliability of multiprocessor systems in the work of zhang et al in 2016 they proposed a new measure for fault diagnosis of systems namely g extra conditional diagnosability it is defined as the diagnosability of a multiprocessor system under the assumption that every fault free component contains more than g vertices which can measure the reliability of interconnection networks in heterogeneous environments more accurately than traditional diagnosability as two kind of favorable topology structures of interconnection networks the n dimensional hypercubes q n and folded hypercubes f q n have many good properties in this paper we investigate their g extra conditional diagnosability and show that a the g extra conditional diagnosability of q n is g 1 n g c g 2 for n 5 and 1 g n 1 4 under the mm model b the g extra conditional diagnosability of f q n is g 1 n c g 2 1 for n 9 and 1 g n 4 under the mm model

constructing one to many disjoint paths in folded hypercubes routing functions have been shown effective in deriving disjoint paths in the hypercube in this paper using a minimal routing function k 1 disjoint paths from one node to another k 1 distinct nodes are constructed in a k dimensional folded hypercube whose maximal length is not greater than the diameter plus one which is minimum in the worst case for the general case the maximal length is nearly optimal spl les the maximal distance between the two end nodes of these k 1 paths plus two as a by product the rabin number of the folded hypercube is obtained which is an open problem raised by s c liaw and g j chang 1999

edge fault tolerance of super edge connectivity for three families of interconnection networks let g v e be a connected graph g is said to be super edge connected or super l for short if every minimum edge cut of g isolates one of the vertex of g a graph g is called m super l if for any edge set s e g with s

on g extra connectivity of folded hypercubes let g be a connected graph and g a non negative integer the g extra connectivity of g is the minimum cardinality of a set of vertices in g if it exists whose deletion disconnects g and leaves each remaining component with more than g vertices in several recent publications the g extra connectivity of an n dimensional folded hypercube was determined for g 3 and some specific n see for example chang tsai and hsieh 2014 4 in this paper an extension of the above results to all 0 g n 1 and n 7 is presented

fault tolerant path embedding in folded hypercubes with both node and edge faults the folded hypercube fq n is a well known variation of the hypercube structure fq n is superior to q n in many measurements such as diameter fault diameter connectivity and so on let email protected fq n resp email protected fq n denote the set of faulty nodes resp faulty edges in fq n in the case that all nodes in fq n are fault free it has been shown that fq n contains a fault free path of length 2 n 1 resp 2 n 2 between any two nodes of odd resp even distance if email protected fq n n 1 where n 1 is odd and fq n contains a fault free path of length 2 n 1 between any two nodes if email protected fq n n 2 where n 2 is even in this paper we extend the above result to obtain two further properties which consider both node and edge faults as follows 1 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 resp 2 n 2 email protected fq n 2 between any two fault free nodes of odd resp even distance if email protected fq n email protected fq n n 1 where n 1 is odd 2 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 between any two fault free nodes if email protected fq n email protected fq n n 2 where n 2 is even

conditional matching preclusion sets abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex in this paper we look for obstruction sets beyond these sets we introduce the conditional matching preclusion number of a graph it is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings we find this number and classify all optimal sets for several basic classes of graphs

bsdes with weak terminal condition we introduce a new class of backward stochastic differential equations in which the t terminal value y t of the solution y z is not fixed as a random variable but only satisfies a weak constraint of the form e psi y t ge m for some possibly random non decreasing map psi and some threshold m we name them textit bsdes with weak terminal condition and obtain a representation of the minimal time t values y t such that y z is a supersolution of the bsde with weak terminal condition it provides a non markovian bsde formulation of the pde characterization obtained for markovian stochastic target problems under controlled loss in bouchard elie and touzi we then study the main properties of this minimal value in particular we analyze its continuity and convexity with respect to the m parameter appearing in the weak terminal condition and show how it can be related to a dual optimal control problem in meyer form these last properties generalize to a non markovian framework previous results on quantile hedging and hedging under loss constraints obtained in follmer and leukert and in bouchard elie and touzi finally we observe a surprisingly strong connection between bsdes with weak terminal condition and 2nd order bsdes in the quasi linear case

the relationship among the specification tests of hausman ramsey and chow abstract this article describes a relationship between the tests for specification error in regression models introduced by ramsey 1969 and hausman 1978 it also shows that the chow 1960 test for structural shift can be viewed as a special case of specification error tests this article shows the common structure of these tests the common basis is the comparison of alternative estimators of regression coefficients under the null hypothesis one estimator is efficient and consistent and the other is consistent the probability limits of the two estimators are different under the alternative hypothesis