Risk-sensitive Portfolio Optimization Research Articles

Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

AbstractIn this paper we consider a discrete‐time risk sensitive portfolio optimization over a long time horizon with proportional transaction costs. We show that within the log‐return i.i.d. framework the solution to a suitable Bellman equation exists under minimal assumptions and can be used to characterize the optimal strategies for both risk‐averse and risk‐seeking cases. Moreover, using numerical examples, we show how a Bellman equation analysis can be used to construct or refine optimal trading strategies in the presence of transaction costs.

Risk-sensitive credit portfolio optimization under partial information and contagion risk

This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we connect the control problem to a quadratic BSDE with jumps, in which the driver term is nonstandard and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and proving uniform a priori estimates, we obtain the existence of a solution to the BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE.

Dynamic risk-sensitive fuzzy asset management with coherent risk measures derived from decision maker’s utility

A dynamic risk-sensitive portfolio optimization problem under risk constraints is discussed by the use of coherent risk measures and fuzzy random variables. Risk-sensitive expected rewards under utility functions are approximated by weighted average value-at-risks, and risk constraints are described by coherent risk measures. The coherent risk measures are represented as weighted average value-at-risks with the best risk spectrum derived from decision maker’s risk-averse utility, and the risk spectrum can inherit the risk-averse property of the decision maker’s utility as weighting. By perception-based extension, the risk-sensitive estimation and coherent risk measures are applied to fuzzy random variables. To find feasible regions of risk constraints, a one-step risk-minimizing problem is investigated by mathematical programming. Next, dynamic risk-sensitive total reward maximization under the feasible coherent risk constraints is discussed by dynamic programming. A few numerical examples are investigated to explain the significance of the obtained results. The proposed method is extremely effective for high-speed portfolio trading.

Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching

We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to b...

Risk-sensitive portfolio optimization problem for a large trader with inside information

We consider a financial model that captures the characteristics of a large trader and an insider. This trader has some influence on the dynamics of prices. Moreover, the information of the insider is the final price plus a blurring noise that disappears as the final time approaches. In such a setting, we try to obtain the explicit solution of a risk-sensitive portfolio optimization problem with a finite time horizon.

The maximum principles for partially observed risk-sensitive optimal controls of Markov regime-switching jump-diffusion system

ABSTRACTThis paper studies partially observed risk-sensitive optimal control problems with correlated noises between the system and the observation. It is assumed that the state process is governed by a continuous-time Markov regime-switching jump-diffusion process and the cost functional is of an exponential-of-integral type. By virtue of a classical spike variational approach, we obtain two general maximum principles for the aforementioned problems. Moreover, under certain convexity assumptions on both the control domain and the Hamiltonian, we give a sufficient condition for the optimality. For illustration, a linear-quadratic risk-sensitive control problem is proposed and solved using the main results. As a natural deduction, a fully observed risk-sensitive maximum principle is also obtained and applied to study a risk-sensitive portfolio optimization problem. Closed-form expressions for both the optimal portfolio and the corresponding optimal cost functional are obtained.

Risk Sensitive Portfolio Optimization in a Jump Diffusion Model with Regimes

This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive portfolio optimization on the finite time horizon. We study the problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth, the maturity, and the risk of aversion parameter.

Long-term optimal portfolios with floor

Long-term risk-sensitive portfolio optimization is studied with floor constraint. A simple rule to characterize its solution is mentioned under a general setting. Following this rule, optimal portfolios are constructed in several ways, using the optimal portfolio without floor constraint, combined with ideas of dynamic portfolio insurance, such as CPPI (constant proportion portfolio insurance), OBPI (option-based portfolio insurance), and DFP (dynamic fund protection). In addition, examples are presented with explicit computations of solutions.

On the Hamilton--Jacobi--Bellman Equation for an Optimal Consumption Problem: I. Existence of Solution

We consider a consumption problem with an infinite time horizon to optimize the discounted expected power utility. The returns and volatilities of the assets are random and affected by some economic factors, modeled as diffusion process. The problem becomes a standard control problem. We derive the Hamilton--Jacobi--Bellman (HJB) equation and study its solutions. In Part I, under some weak conditions we prove the existence of a solution for this HJB equation when we assume the existence of an ordered pair of sub/supersolution. To construct an ordered pair of sub/supersolution, we also consider the risk-sensitive portfolio optimization problem. In Part II [Hata and Sheu, SIAM J. Control Optim., 50 (2012), pp. 2401--2430], we consider the uniqueness of the solution and prove the verification theorem.

Optimal portfolio for a highly risk-averse investor: A differential game interpretation

Risk-sensitive portfolio optimization is treated with a linear-Gaussian-factor model. The main interest is how a highly risk-averse investor controls his/her interest rate risk. A simple risk-averse limit with increasing risk-averse parameter γ ↑ ∞ is not appropriate: the associated maximized risk-sensitized expected growth rate goes to −∞ as γ ↑ ∞, and a “breakdown” occurs in the limit. Instead, a small-noise and large-risk-aversion limit is considered, assuming the factor-noise has a small parameter e 1, taking e-dependent risk-averse parameter γ(e) = O(e−2) 1, and letting e ↓ 0. The limit value is characterized as the value of a linear-quadratic differential game. A sequence (π(e))e>0 of e-dependent dynamic investment strategies is constructed from a saddle point of the game, and its asymptotic optimality is shown as e ↓ 0.

Risk-Sensitive Portfolio Optimization and Its Applications

Risk-Sensitive Portfolio Optimization and Its Applications

Risk-sensitive portfolio optimization problems for hidden Markov factors on infinite time horizon

Risk-sensitive portfolio optimization problems for hidden Markov factors on infinite time horizon

Risk-sensitive Portfolio Optimization with Two-factor Having a Memory Effect

Risk-sensitive portfolio optimization problems are studied with a specific setting: a market model with a two-dimensional linear-factor is considered, where the factor consisits of an Ornshtein-Uhlenbeck process and its historic weighted-average. A sharp solvability condition is obtained in risk-seeking case. Further, an application of CPPI technique is mentioned to treat a problem with floor-constraint.

“Down-Side Risk” Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates

With a bank account and a risky stock, both of which are affected by Cox-Ingersoll-Ross’s interest rates, we treat two “down-side risk” minimization problems of the large deviation probability for long-term investment. Explicit solutions of the problems are given by solving the associated risk-sensitive portfolio optimization problems.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Risk-Sensitive Portfolio Optimization Problems with Fixed Income Securities

We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai (SIAM J. Control Optim. 41:1779–1800, 2003). The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of an optimal portfolio in both finite-horizon and infinite-horizon problems.

Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs

Discrete time risk sensitive portfolio optimization with consumption and proportional transaction costs

Risk-Sensitive Portfolio Optimization With Completely and Partially Observed Factors

In this note, optimal portfolio maximizing the long run risk-sensitized growth rate of the capital process in the case when the dynamics of the asset prices depend on some economical factors, which are completely or partially observed, using a discounted cost approach is shown.

Risk-sensitive portfolio optimization with transaction costs

We develop methods of risk-sensitive impulsive control theory in order to solve an optimal asset allocation problem with transaction costs and a stochastic interest rate. The optimal trading strategy and the risk-sensitized expected exponential growth rate of the investor’s portfolio are characterized in terms of a non-linear quasi-variational inequality. This problem can then be interpreted as the ergodic Isaac–Hamilton–Jacobi equation associated with a min–max problem. We use a numerical method based on an extended two-stage policy iteration algorithm for min–max problems and provide numerical results for the case of two assets and one factor that is a Vasicek interest rate.

Optimal Strategies for Risk-Sensitive Portfolio Optimization Problems for General Factor Models

We consider constructing optimal strategies for risk-sensitive portfolio optimization problems on an infinite time horizon for general factor models, where the mean returns and the volatilities of individual securities or asset categories are explicitly affected by economic factors. The factors areassumed to be general diffusion processes. In studying the ergodic type Bellman equations of the risk-sensitive portfolio optimization problems, we introduce some auxiliary classical stochastic control problems with the same Bellman equations as the original ones. We show that the optimal diffusion processes of the problem are ergodic and that under some condition related to integrability by the invariant measures of the diffusion processes we can construct optimal strategies for the original problems by using the solution of the Bellman equations.