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 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.

NATURAL GAS-FIRED POWER PLANTS VALUATION AND OPTIMIZATION UNDER LÉVY COPULAS AND REGIME SWITCHING

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
NEMAT SAFAROV ◽  
COLIN ATKINSON
Keyword(s):  
Natural Gas ◽  
Regime Switching ◽  
Power Plants ◽  
Control Strategies ◽  
Numerical Approach ◽  
Spot Price ◽  
Operating Characteristics ◽  
Hjb Equations ◽  
Explicit Finite Difference ◽  
Hamilton Jacobi Bellman

In this work, we analyze a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Lévy regime-switching model incorporates the effects of demand-supply fluctuations in energy markets and abrupt economic disruptions or business cycles. We make use of skewed Lévy copulas to model the dependence risk of electricity and gas jumps. The corresponding coupled Hamilton–Jacobi–Bellman (HJB) equations are solved by an explicit finite difference method. The numerical approach gives us both the value of the plant and its optimal operating strategy depending on the gas and electricity prices, current temperature of the boiler and time. The surfaces of control strategies and contract values are obtained by implementing the numerical method for a particular example.

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.

WORST-CASE PORTFOLIO OPTIMIZATION IN A MARKET WITH BUBBLES

2016 ◽  
Vol 19 (02) ◽  
pp. 1650009 ◽  
Author(s):  
CHRISTOPH BELAK ◽  
SÖREN CHRISTENSEN ◽  
OLAF MENKENS
Keyword(s):  
Regime Switching ◽  
Asset Price ◽  
Optimal Strategies ◽  
Coupled System ◽  
Maximization Problem ◽  
Worst Case ◽  
Bellman Equations ◽  
Asset Price Bubbles ◽  
Price Bubbles ◽  
Hamilton Jacobi Bellman

We investigate a utility maximization problem in the presence of asset price bubbles. At random times, the investor receives warnings that a bubble has formed in the market which may lead to a crash in the risky asset. We propose a regime-switching model for the warnings and we make no assumptions about the distribution of the timing and the size of the crashes. Instead, we assume that the investor takes a worst-case perspective towards their impacts, i.e. the investor maximizes her expected utility under the worst-case crash scenario. We characterize the value function by a system of Hamilton–Jacobi–Bellman equations and derive a coupled system of ordinary differential equations for the optimal strategies. Numerical examples are provided.

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.

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 Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

scholarly journals An Analytic Approach for Pricing American Options with Regime Switching

2021 ◽  
Vol 14 (5) ◽  
pp. 188
Author(s):  
Leunglung Chan ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
American Options ◽  
Option Price ◽  
Switching Model ◽  
Homotopy Analysis ◽  
State Regime ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Hidden States

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

Sign in / Sign up

Export Citation Format

Share Document