OPTIMAL DYNAMIC FUTURES PORTFOLIO UNDER A MULTIFACTOR GAUSSIAN FRAMEWORK

2021 ◽  
pp. 2150028
Author(s):  
TIM LEUNG ◽  
RAPHAEL YAN ◽  
YANG ZHOU
Keyword(s):  
Continuous Time ◽  
Utility Maximization ◽  
Asset Price ◽  
Factor Models ◽  
Central Tendency ◽  
Futures Trading ◽  
Hjb Equations ◽  
Stochastic Framework ◽  
Optimal Dynamic ◽  
Hamilton Jacobi Bellman

We study the problem of dynamically trading futures in continuous time under a multifactor Gaussian framework. We present a utility maximization approach to determine the optimal futures trading strategy. This leads to the explicit solution to the Hamilton–Jacobi–Bellman (HJB) equations. We apply our stochastic framework to two-factor models, namely, the Schwartz model and Central Tendency Ornstein–Uhlenbeck (CTOU) model. We also develop a multiscale CTOU model, which has a fast mean-reverting and a slow mean-reverting factor in the spot asset price dynamics. Numerical examples are provided to illustrate the investor’s optimal positions for different futures portfolios.

scholarly journals Optimal dynamic futures portfolio in a regime-switching market framework

2019 ◽  
Vol 06 (04) ◽  
pp. 1950034
Author(s):  
Tim Leung ◽  
Yang Zhou
Keyword(s):  
Regime Switching ◽  
Asset Price ◽  
Futures Trading ◽  
Hjb Equations ◽  
Market Framework ◽  
Stochastic Framework ◽  
Optimal Dynamic ◽  
Market Regimes ◽  
Markov Modulated ◽  
Hamilton Jacobi Bellman

We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures trading strategy. This leads to the analysis of the associated system of Hamilton–Jacobi–Bellman (HJB) equations, which are reduced to a system of linear ODEs. We apply our stochastic framework to two models, namely, the Regime-Switching Geometric Brownian Motion (RS-GBM) model and Regime-Switching Exponential Ornstein–Uhlenbeck (RS-XOU) model. Numerical examples are provided to illustrate the investor’s optimal futures positions and portfolio value across market regimes.

Optimal dynamic pairs trading of futures under a two-factor mean-reverting model

2018 ◽  
Vol 05 (03) ◽  
pp. 1850027 ◽  
Author(s):  
Tim Leung ◽  
Raphael Yan
Keyword(s):  
Utility Maximization ◽  
Futures Contracts ◽  
Spot Price ◽  
Maximization Problem ◽  
Pairs Trading ◽  
Futures Trading ◽  
Vix Futures ◽  
Optimal Dynamic ◽  
Hamilton Jacobi Bellman ◽  
Utility Maximization Problem

We study the problem of dynamically trading a pair of futures contracts. We consider a two-factor mean-reverting model, where the spot price tends to evolve around its stochastic equilibrium that is also mean-reverting. We derive the futures price dynamics and determine the optimal futures trading strategy by solving a utility maximization problem. By analyzing the associated Hamilton–Jacobi–Bellman equation, we solve the utility maximization explicitly and provide the optimal trading strategies in closed form. Our strategies are applied to volatility (VIX) futures trading, and illustrated in a series of numerical examples.

scholarly journals Finite Difference Methods for the Hamilton–Jacobi–Bellman Equations Arising in Regime Switching Utility Maximization

2020 ◽  
Vol 85 (3) ◽  
Author(s):  
Jingtang Ma ◽  
Jianjun Ma
Keyword(s):  
Finite Difference ◽  
Regime Switching ◽  
Utility Maximization ◽  
Finite Difference Methods ◽  
Hjb Equations ◽  
Functional Operator ◽  
Bellman Equations ◽  
Numerical Comparisons ◽  
Difference Methods ◽  
Hamilton Jacobi Bellman

AbstractFor solving the regime switching utility maximization, Fu et al. (Eur J Oper Res 233:184–192, 2014) derive a framework that reduce the coupled Hamilton–Jacobi–Bellman (HJB) equations into a sequence of decoupled HJB equations through introducing a functional operator. The aim of this paper is to develop the iterative finite difference methods (FDMs) with iteration policy to the sequence of decoupled HJB equations derived by Fu et al. (2014). The convergence of the approach is proved and in the proof a number of difficulties are overcome, which are caused by the errors from the iterative FDMs and the policy iterations. Numerical comparisons are made to show that it takes less time to solve the sequence of decoupled HJB equations than the coupled ones.

scholarly journals PORTFOLIO OPTIMIZATION IN AFFINE MODELS WITH MARKOV SWITCHING

2015 ◽  
Vol 18 (05) ◽  
pp. 1550030 ◽  
Author(s):  
MARCOS ESCOBAR ◽  
DANIELA NEYKOVA ◽  
RUDI ZAGST
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Asset Price ◽  
Heston Model ◽  
Investment Horizon ◽  
Investment Strategies ◽  
Affine Structure ◽  
Financial Model ◽  
Hjb Equations ◽  
Stochastic Factor ◽  
Hamilton Jacobi Bellman

We consider a stochastic-factor financial model wherein the asset price and the stochastic-factor processes depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this end we apply Merton's approach, because we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains, we first derive the Hamilton–Jacobi–Bellman (HJB) equations that, in our case, correspond to a system of coupled nonlinear partial differential equations (PDE). Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage, we propose a separable ansatz that leads to explicit solutions. General verification results are also proved. The results are illustrated for the special case of a Markov-modulated Heston model.

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Shou Chen ◽  
Shengpeng Xiang ◽  
Hongbo He
Keyword(s):  
Absolute Risk ◽  
Hyperbolic Discounting ◽  
Time Preferences ◽  
Hjb Equations ◽  
Portfolio Decisions ◽  
Special Cases ◽  
Intertemporal Consumption ◽  
Hamilton Jacobi Bellman ◽  
Hara Utility ◽  
Exponential Discounting

Abstract We study the intertemporal consumption and portfolio rules in the model with the general hyperbolic absolute risk aversion (HARA) utility. The equivalent approximation approach is employed to obtain the Hamilton-Jacobi-Bellman (HJB) equations, and a remarkable property is shown: portfolio rules are independent of the discount function. Moreover, both the consumption and portfolio rates are non-increasing functions of wealth. Particularly illustrative cases examined in detail are the models with the most adopted discount functions, including exponential discounting and hyperbolic discounting. Explicit solutions for intertemporal decisions are found for these special cases, revealing that individual’s time preferences affect the consumption rules only. Moreover, the time-consistent consumption rate under hyperbolic discounting is larger than its counterpart under exponential discounting.

scholarly journals Portfolio Optimization with Asset-Liability Ratio Regulation Constraints

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
De-Lei Sheng ◽  
Peilong Shen
Keyword(s):  
High Speed ◽  
Asset Price ◽  
Investment Strategy ◽  
Minimum Variance ◽  
Control Technique ◽  
Duality Method ◽  
Lagrange Duality ◽  
Short Period ◽  
High Investment ◽  
Hamilton Jacobi Bellman

This paper considers both a top regulation bound and a bottom regulation bound imposed on the asset-liability ratio at the regulatory time T to reduce risks of abnormal high-speed growth of asset price within a short period of time (or high investment leverage), and to mitigate risks of low assets’ return (or a sharp fall). Applying the stochastic optimal control technique, a Hamilton–Jacobi–Bellman (HJB) equation is derived. Then, the effective investment strategy and the minimum variance are obtained explicitly by using the Lagrange duality method. Moreover, some numerical examples are provided to verify the effectiveness of our results.

UTILITY MAXIMIZATION IN A PURE JUMP MODEL WITH PARTIAL OBSERVATION

2010 ◽  
Vol 25 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Paola Tardelli
Keyword(s):  
Utility Maximization ◽  
Point Processes ◽  
Marked Point ◽  
Asset Price ◽  
Main Tool ◽  
Risky Asset ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
Underlying Event ◽  
Jump Model

This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process—a marked point process having common jump times with the risky asset price process. The problem of utility maximization of terminal wealth is dealt with when the underlying event arrivals process is assumed to be unobserved by the market agents using, as the main tool, backward stochastic differential equations. The dual problem is studied. Explicit solutions in a particular case are given.

Sign in / Sign up

Export Citation Format

Share Document