# Maximum principles for jump diffusion processes with infinite horizon

@article{Haadem2012MaximumPF, title={Maximum principles for jump diffusion processes with infinite horizon}, author={Sven Haadem and Bernt {\O}ksendal and Frank Proske}, journal={Autom.}, year={2012}, volume={49}, pages={2267-2275} }

## 36 Citations

### A Maximum Principle for Infinite Horizon Delay Equations

- Mathematics, EconomicsSIAM J. Math. Anal.
- 2013

A maximum principle of optimal control of stochastic delay equations on infinite horizon is proved and an application to the optimal consumption rate from an economic quantity is illustrated.

### Infinite horizon optimal control of forward-backward stochastic differential equations with delay

- MathematicsJ. Comput. Appl. Math.
- 2014

### Infinite horizon mean-field type forward backward stochastic delay differential game with Poisson jump processes

- MathematicsMalaya Journal of Matematik
- 2019

This paper analyzes the optimal control of mean field type forward-backward non-zero sum stochastic delay differential game with Poisson random measure over infinite time horizon. Further, infinite…

### Infinite horizon optimal control of mean-field forward-backward delayed systems with Poisson jumps

- MathematicsEur. J. Control
- 2019

### Infinite horizon optimal control of forward–backward stochastic system driven by Teugels martingales with Lévy processes

- Mathematics
- 2017

In this paper, we consider the infinite horizon nonlinear optimal control of forward–backward stochastic system governed by Teugels martingales associated with Levy processes and one dimensional…

### Future Expectations Modeling, Random Coefficient Forward-Backward Stochastic Differential Equations, and Stochastic Viscosity Solutions

- MathematicsMath. Oper. Res.
- 2020

A class of infinite horizon fully coupled forward–backward stochastic differential equations (FBSDEs) with random coefficients that are stimulated by various continuous time fluctuations are studied.

### Mean-field delayed BSDEs in finite and infinite horizon

- Mathematics
- 2015

We establish sufficient conditions for the existence and uniqueness of different types of delayed BSDEs in finite time horizon. We consider then infinite horizon, replacing the terminal value…

### Sufficient Stochastic Maximum Principle for Discounted Control Problem

- Mathematics
- 2011

The sufficient Pontryagin’s maximum principle for infinite horizon discounted stochastic control problem is established and it is assumed that the control domain $$U$$U is a convex bounded set and the control may enter the diffusion term of the state equation.

### Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance

- MathematicsAutom.
- 2014

### Infinite horizon optimal control of mean-field delay system with semi-Markov modulated jump-diffusion processes

- MathematicsThe Journal of Analysis
- 2018

This paper describes the study of infinite horizon optimal control of stochastic delay differential equation with semi-Markov modulated jump-diffusion processes in which the control domain is not…

## References

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### A Maximum Principle for Infinite Horizon Delay Equations

- Mathematics, EconomicsSIAM J. Math. Anal.
- 2013

A maximum principle of optimal control of stochastic delay equations on infinite horizon is proved and an application to the optimal consumption rate from an economic quantity is illustrated.

### A Maximum Principle for Stochastic Control with Partial Information

- Mathematics
- 2007

Abstract We study the problem of optimal control of a jump diffusion, that is, a process which is the solution of a stochastic differential equation driven by Lévy processes. It is required that the…

### Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps

- Mathematics
- 1994

A maximum principle is proved for optimal controls of stochastic systems with random jumps. The control is allowed to enter into both diffusion and jump terms. The form of the maximum principle turns…

### The maximum principle for stochastic control with partial information

- Mathematics1986 25th IEEE Conference on Decision and Control
- 1986

In this paper a Pontryagin-type maximum principle is given for the following stochastic optimal control problem: the state of the system satisfies (i.e. is a weak solution of) an Ito equation with…

### Necessary conditions for optimal control problems with infinite horizons

- Mathematics
- 1974

Abstract : In a classical optimal control problem the terminal time, either prescribed a priori or not, is always a real number. In many dynamic optimization problems in economics one is lead to…

### Backward stochastic differential equations and integral-partial differential equations

- Mathematics
- 1997

We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the…

### Backward Stochastic Ddifferential Equations with Jumps and Related Non Linear Expectations

- Mathematics
- 2004

### Financial Modelling with Jump Processes

- Mathematics
- 2003

WINNER of a Riskbook.com Best of 2004 Book Award!During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has…