pwc-archive/papers-with-abstracts huggingface dataset:
Bayesian optimal investment and reinsurance with dependent financial and insurance risks
Authors: Nicole Bäuerle, Gregor Leimcke
Date: 2021-02-18 00:00:00

Major events like natural catastrophes or the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined it is important to consider models which reflect this dependence. In this paper we make a proposal how to generate dependence between the financial market and claim sizes in times of crisis and determine via a stochastic control approach an optimal investment and reinsurance strategy which maximizes the expected exponential utility of terminal wealth. Moreover, we also allow that the claim size distribution may be learned in the model. We give comparisons and bounds on the optimal strategy using simple models. What turns out to be very surprising is that numerical results indicate that even a minimal dependence which is created in this model has a huge impact on the control in the sense that the insurer is much more prudent then.
Deep Reinforcement Learning for Portfolio Optimization using Latent Feature State Space (LFSS) Module
Authors: Kumar Yashaswi
Date: 2021-02-11 00:00:00
Tasks: Decision Making, Deep Reinforcement Learning, Portfolio Optimization, reinforcement-learning, Reinforcement Learning (RL), Sequential Decision Making, Time Series Analysis

Dynamic Portfolio optimization is the process of distribution and rebalancing of a fund into different financial assets such as stocks, cryptocurrencies, etc, in consecutive trading periods to maximize accumulated profits or minimize risks over a time horizon. This field saw huge developments in recent years, because of the increased computational power and increased research in sequential decision making through control theory. Recently Reinforcement Learning(RL) has been an important tool in the development of sequential and dynamic portfolio optimization theory. In this paper, we design a Deep Reinforcement Learning(DRL) framework as an autonomous portfolio optimization agent consisting of a Latent Feature State Space(LFSS) Module for filtering and feature extraction of financial data which is used as a state space for deep RL model. We develop an extensive RL agent with high efficiency and performance advantages over several benchmarks and model-free RL agents used in prior work. The noisy and non-stationary behaviour of daily asset prices in the financial market is addressed through Kalman Filter. Autoencoders, ZoomSVD, and restricted Boltzmann machines were the models used and compared in the module to extract relevant time series features as state space. We simulate weekly data, with practical constraints and transaction costs, on a portfolio of S&P 500 stocks. We introduce a new benchmark based on technical indicator Kd-Index and Mean-Variance Model as compared to equal weighted portfolio used in most of the prior work. The study confirms that the proposed RL portfolio agent with state space function in the form of LFSS module gives robust results with an attractive performance profile over baseline RL agents and given benchmarks.
FRM Financial Risk Meter for Emerging Markets
Authors: Souhir Ben Amor, Michael Althof, Wolfgang Karl Härdle
Date: 2021-02-10 00:00:00
Tasks: Portfolio Optimization

The fast-growing Emerging Market (EM) economies and their improved transparency and liquidity have attracted international investors. However, the external price shocks can result in a higher level of volatility as well as domestic policy instability. Therefore, an efficient risk measure and hedging strategies are needed to help investors protect their investments against this risk. In this paper, a daily systemic risk measure, called FRM (Financial Risk Meter) is proposed. The FRM-EM is applied to capture systemic risk behavior embedded in the returns of the 25 largest EMs FIs, covering the BRIMST (Brazil, Russia, India, Mexico, South Africa, and Turkey), and thereby reflects the financial linkages between these economies. Concerning the Macro factors, in addition to the Adrian and Brunnermeier (2016) Macro, we include the EM sovereign yield spread over respective US Treasuries and the above-mentioned countries currencies. The results indicated that the FRM of EMs FIs reached its maximum during the US financial crisis following by COVID 19 crisis and the Macro factors explain the BRIMST FIs with various degrees of sensibility. We then study the relationship between those factors and the tail event network behavior to build our policy recommendations to help the investors to choose the suitable market for in-vestment and tail-event optimized portfolios. For that purpose, an overlapping region between portfolio optimization strategies and FRM network centrality is developed. We propose a robust and well-diversified tail-event and cluster risk-sensitive portfolio allocation model and compare it to more classical approaches
Portfolio Construction Using Stratified Models
Authors: Jonathan Tuck, Shane Barratt, Stephen Boyd
Date: 2021-01-11 00:00:00

In this paper we develop models of asset return mean and covariance that depend on some observable market conditions, and use these to construct a trading policy that depends on these conditions, and the current portfolio holdings. After discretizing the market conditions, we fit Laplacian regularized stratified models for the return mean and covariance. These models have a different mean and covariance for each market condition, but are regularized so that nearby market conditions have similar models. This technique allows us to fit models for market conditions that have not occurred in the training data, by borrowing strength from nearby market conditions for which we do have data. These models are combined with a Markowitz-inspired optimization method to yield a trading policy that is based on market conditions. We illustrate our method on a small universe of 18 ETFs, using three well known and publicly available market variables to construct 1000 market conditions, and show that it performs well out of sample. The method, however, is general, and scales to much larger problems, that presumably would use proprietary data sources and forecasts along with publicly available data.
Deep learning for efficient frontier calculation in finance
Authors: Xavier Warin
Date: 2021-01-06 00:00:00
Tasks: Deep Learning, Portfolio Optimization

We propose deep neural network algorithms to calculate efficient frontier in some Mean-Variance and Mean-CVaR portfolio optimization problems. We show that we are able to deal with such problems when both the dimension of the state and the dimension of the control are high. Adding some additional constraints, we compare different formulations and show that a new projected feedforward network is able to deal with some global constraints on the weights of the portfolio while outperforming classical penalization methods. All developed formulations are compared in between. Depending on the problem and its dimension, some formulations may be preferred.
Portfolio optimization with two quasiconvex risk measures
Authors: Çağın Ararat
Date: 2020-12-11 00:00:00
Tasks: Portfolio Optimization, Vocal Bursts Valence Prediction

We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is necessary to consider the risk preferences of two parties, such as a portfolio manager and a regulator, at the same time. A special case of this problem where the risk measures are assumed to be coherent (positively homogeneous) is studied recently in a joint work of the author. The present paper extends the analysis to a more general setting by assuming that the two risk measures are only quasiconvex. First, we study the case where the principal risk measure is convex. We introduce a dual problem, show that there is zero duality gap between the portfolio optimization problem and the dual problem, and finally identify a condition under which the Lagrange multiplier associated to the dual problem at optimality gives an optimal portfolio. Next, we study the general case without the convexity assumption and show that an approximately optimal solution with prescribed optimality gap can be achieved by using the well-known bisection algorithm combined with a duality result that we prove.
Personalized Robo-Advising: Enhancing Investment through Client Interaction
Authors: Agostino Capponi, Sveinn Olafsson, Thaleia Zariphopoulou
Date: 2019-11-04 00:00:00
Tasks: Portfolio Optimization

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a novel framework, in which a robo-advisor interacts with a client to solve an adaptive mean-variance portfolio optimization problem. The risk-return tradeoff adapts to the client's risk profile, which depends on idiosyncratic characteristics, market returns, and economic conditions. We show that the optimal investment strategy includes both myopic and intertemporal hedging terms which are impacted by the dynamics of the client's risk profile. We characterize the optimal portfolio personalization via a tradeoff faced by the robo-advisor between receiving client information in a timely manner and mitigating behavioral biases in the risk profile communicated by the client. We argue that the optimal portfolio's Sharpe ratio and return distribution improve if the robo-advisor counters the client's tendency to reduce market exposure during economic contractions when the market risk-return tradeoff is more favorable.
Price Impact on Term Structure
Authors: Damiano Brigo, Federico Graceffa, Eyal Neuman
Date: 2020-11-19 00:00:00

We introduce a first theory of price impact in presence of an interest-rates term structure. We explain how one can formulate instantaneous and transient price impact on bonds with different maturities, including a cross price impact that is endogenous to the term structure. We connect the introduced impact to classic no-arbitrage theory for interest rate markets, showing that impact can be embedded in the pricing measure and that no-arbitrage can be preserved. We present pricing examples in presence of price impact and numerical examples of how impact changes the shape of the term structure. Finally, to show that our approach is applicable we solve an optimal execution problem in interest rate markets with the type of price impact we developed in the paper.
Portfolio Optimisation Using the D-Wave Quantum Annealer
Authors: Frank Phillipson, Harshil Singh Bhatia
Date: 2020-11-13 00:00:00

The first quantum computers are expected to perform well at quadratic optimisation problems. In this paper a quadratic problem in finance is taken, the Portfolio Optimisation problem. Here, a set of assets is chosen for investment, such that the total risk is minimised, a minimum return is realised and a budget constraint is met. This problem is solved for several instances in two main indices, the Nikkei225 and the S\&P500 index, using the state-of-the-art implementation of D-Wave's quantum annealer and its hybrid solvers. The results are benchmarked against conventional, state-of-the-art, commercially available tooling. Results show that for problems of the size of the used instances, the D-Wave solution, in its current, still limited size, comes already close to the performance of commercial solvers.
The importance of dynamic risk constraints for limited liability operators
Authors: John Armstrong, Damiano Brigo, Alex S. L. Tse
Date: 2020-11-06 00:00:00

Previous literature shows that prevalent risk measures such as Value at Risk or Expected Shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio optimisation. However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the asset performance, the trader's portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market.
Optimal Portfolio Using Factor Graphical Lasso
Authors: Tae-Hwy Lee, Ekaterina Seregina
Date: 2020-11-01 00:00:00

Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix. However, when stock returns are driven by common factors, such assumption does not hold. We address this limitation and develop a framework, Factor Graphical Lasso (FGL), which integrates graphical models with the factor structure in the context of portfolio allocation by decomposing a precision matrix into low-rank and sparse components. Our theoretical results and simulations show that FGL consistently estimates the portfolio weights and risk exposure and also that FGL is robust to heavy-tailed distributions which makes our method suitable for financial applications. FGL-based portfolios are shown to exhibit superior performance over several prominent competitors including equal-weighted and Index portfolios in the empirical application for the S&P500 constituents.
A Basket Half Full: Sparse Portfolios
Authors: Ekaterina Seregina
Date: 2020-11-05 00:00:00

The existing approaches to sparse wealth allocations (1) are limited to low-dimensional setup when the number of assets is less than the sample size; (2) lack theoretical analysis of sparse wealth allocations and their impact on portfolio exposure; (3) are suboptimal due to the bias induced by an $\ell_1$-penalty. We address these shortcomings and develop an approach to construct sparse portfolios in high dimensions. Our contribution is twofold: from the theoretical perspective, we establish the oracle bounds of sparse weight estimators and provide guidance regarding their distribution. From the empirical perspective, we examine the merit of sparse portfolios during different market scenarios. We find that in contrast to non-sparse counterparts, our strategy is robust to recessions and can be used as a hedging vehicle during such times.
Rule-based Strategies for Dynamic Life Cycle Investment
Authors: T. R. B. den Haan, K. W. Chau, M. van der Schans, C. W. Oosterlee
Date: 2020-11-05 00:00:00

In this work, we consider rule-based investment strategies for managing a defined contribution saving scheme under the Dutch pension fund testing model. We found that dynamic rule-based investment can outperform traditional static strategies, by which we mean that the pensioner can achieve the target retirement income with higher probability and limit the shortfall when target is not met. In comparison with the popular dynamic programming technique, the rule-based strategy has a more stable asset allocation throughout time and avoid excessive transactions, which may be hard to explain to the investor. We also study a combined strategy of rule based target and dynamic programming in this work. Another key feature of this work is that there is no risk-free asset under our setting, instead, a matching portfolio is introduced for the investor to avoid unnecessary risk.
From small markets to big markets
Authors: Laurence Carassus, Miklos Rasonyi
Date: 2019-07-12 00:00:00

We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising expected utility in this setting. Besides establishing the existence of optimizers under weaker assumptions than previous papers, we go on studying the relationship between optimal investments in finite market segments and those in the whole market. We show that certain natural (but nontrivial) continuity rules hold: maximal satisfaction, reservation prices and (convex combinations of) optimizers computed in small markets converge to their respective counterparts in the big market.
Optimal Order Execution in Intraday Markets: Minimizing Costs in Trade Trajectories
Authors: Christopher Kath, Florian Ziel
Date: 2020-09-16 00:00:00
Tasks: Position

Optimal execution, i.e., the determination of the most cost-effective way to trade volumes in continuous trading sessions, has been a topic of interest in the equity trading world for years. Electricity intraday trading slowly follows this trend but is far from being well-researched. The underlying problem is a very complex one. Energy traders, producers, and electricity wholesale companies receive various position updates from customer businesses, renewable energy production, or plant outages and need to trade these positions in intraday markets. They have a variety of options when it comes to position sizing or timing. Is it better to trade all amounts at once? Should they split orders into smaller pieces? Taking the German continuous hourly intraday market as an example, this paper derives an appropriate model for electricity trading. We present our results from an out-of-sample study and differentiate between simple benchmark models and our more refined optimization approach that takes into account order book depth, time to delivery, and different trading regimes like XBID (Cross-Border Intraday Project) trading. Our paper is highly relevant as it contributes further insight into the academic discussion of algorithmic execution in continuous intraday markets and serves as an orientation for practitioners. Our initial results suggest that optimal execution strategies have a considerable monetary impact.
Forward utilities and Mean-field games under relative performance concerns
Authors: Goncalo dos Reis, Vadim Platonov
Date: 2020-05-16 00:00:00
Tasks: Management, Model Selection

We introduce the concept of mean field games for agents using Forward utilities of CARA type to study a family of portfolio management problems under relative performance concerns. Under asset specialization of the fund managers, we solve the forward-utility finite player game and the forward-utility mean-field game. We study best response and equilibrium strategies in the single common stock asset and the asset specialization with common noise. As an application, we draw on the core features of the forward utility paradigm and discuss a problem of time-consistent mean-field dynamic model selection in sequential time-horizons.
Solving High-Order Portfolios via Successive Convex Approximation Algorithms
Authors: Rui Zhou, Daniel P. Palomar
Date: 2020-08-03 00:00:00
Tasks: Vocal Bursts Intensity Prediction

The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments.
Optimal Investment, Heterogeneous Consumption and Best Time for Retirement
Authors: Hyun Jin Jang, Zuo Quan Xu, Harry Zheng
Date: 2020-08-02 00:00:00

This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.
A fully data-driven approach to minimizing CVaR for portfolio of assets via SGLD with discontinuous updating
Authors: Sotirios Sabanis, Ying Zhang
Date: 2020-07-02 00:00:00
Tasks: Stochastic Optimization

A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of possibly complicated, high-dimensional landscapes. With this in mind, we extend here the non-asymptotic analysis of SGLD to the case of discontinuous stochastic gradients. We are thus able to provide theoretical guarantees for the algorithm's convergence in (standard) Wasserstein distances for both convex and non-convex objective functions. We also provide explicit upper estimates of the expected excess risk associated with the approximation of global minimizers of these objective functions. All these findings allow us to devise and present a fully data-driven approach for the optimal allocation of weights for the minimization of CVaR of portfolio of assets with complete theoretical guarantees for its performance. Numerical results illustrate our main findings.