A maximum principle for controlled stochastic factor model

2018 ◽  
Vol 24 (2) ◽  
pp. 495-517
Author(s):  
Virginie Konlack Socgnia ◽  
Olivier Menoukeu Pamen
Keyword(s):  
Differential Equation ◽  
Maximum Principle ◽  
Control Problem ◽  
Factor Model ◽  
Convenience Yield ◽  
Filtering Technique ◽  
Stochastic Factor ◽  
Hedging Problem ◽  
Stochastic Factor Model ◽  
Sufficient Maximum Principle

In the present work, we consider an optimal control for a three-factor stochastic factor model. We assume that one of the factors is not observed and use classical filtering technique to transform the partial observation control problem for stochastic differential equation (SDE) to a full observation control problem for stochastic partial differential equation (SPDE). We then give a sufficient maximum principle for a system of controlled SDEs and degenerate SPDE. We also derive an equivalent stochastic maximum principle. We apply the obtained results to study a pricing and hedging problem of a commodity derivative at a given location, when the convenience yield is not observable.

scholarly journals An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications

2020 ◽  
Vol 28 (1) ◽  
pp. 1-18
Author(s):  
Dahbia Hafayed ◽  
Adel Chala
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Doubly Stochastic ◽  
Risk Sensitive ◽  
Performance Functional

AbstractIn this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.

scholarly journals An optimal consumption and investment problem with partial information

2018 ◽  
Vol 50 (01) ◽  
pp. 131-153 ◽  
Author(s):  
Hiroaki Hata ◽  
Shuenn-Jyi Sheu
Keyword(s):  
Partial Information ◽  
Factor Model ◽  
Absolute Risk ◽  
Optimal Consumption ◽  
Martingale Method ◽  
Risky Assets ◽  
Time Optimal ◽  
Stochastic Factor ◽  
Stochastic Factor Model ◽  
Optimal Consumption And Investment

AbstractWe consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of consumption and terminal wealth. We treat a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case in which the investor cannot observe the factor process and uses only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. We derive the Hamilton–Jacobi–Bellman equation. We solve this equation to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce the results obtained by the martingale method.

scholarly journals A GENERAL OPTIMAL INVESTMENT MODEL IN THE PRESENCE OF BACKGROUND RISK

2016 ◽  
Vol 11 (01) ◽  
pp. 1650001 ◽  
Author(s):  
MOAWIA ALGHALITH ◽  
XU GUO ◽  
WING-KEUNG WONG ◽  
LIXING ZHU
Keyword(s):  
Utility Function ◽  
Dynamic Model ◽  
Dynamic Models ◽  
Factor Model ◽  
Optimal Investment ◽  
Background Risk ◽  
Investment Model ◽  
General Utility ◽  
Stochastic Factor ◽  
Stochastic Factor Model

In this paper we present two dynamic models of background risk. We first present a stochastic factor model with an additive background risk. Then, we present a dynamic model of simultaneous (correlated) multiplicative background risk and additive background risk. In so doing, we use a general utility function.

scholarly journals The maximum principle for a type of hereditary semilinear differential equation

1994 ◽  
Vol 36 (2) ◽  
pp. 194-212
Author(s):  
Feiyue He
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
The Maximum Principle ◽  
Semilinear Differential Equation

AbstractAn optimal control problem governed by a class of delay semilinear differential equations is studied. The existence of an optimal control is proven, and the maximum principle and approximating schemes are found. As applications, three examples are discussed.

THE INTERACTION BETWEEN THE FINANCIAL SECTOR AND THE REAL SECTOR: A STOCHASTIC MODEL

2012 ◽  
Vol 07 (02) ◽  
pp. 1250009
Author(s):  
MOAWIA ALGHALITH ◽  
TRACY POLIUS
Keyword(s):  
Stock Market ◽  
Stochastic Model ◽  
Financial Market ◽  
Factor Model ◽  
Financial Sector ◽  
Real Sector ◽  
The Real ◽  
Real Gdp ◽  
Stochastic Factor ◽  
Stochastic Factor Model

Using a stochastic factor model, we devise a method to estimate the marginal impact of real GDP on the stock market. We apply our approach to the Jamaican financial market.

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