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A Maximum Principle for Infinite Horizon Delay Equations

Nacira Agram · Sven Haadem · Bernt Øksendal · Frank Proske

62 citations0/0 files storedSIAM Journal on Mathematical Analysis

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stability and Controllability of Differential Equations

Abstract

We prove a maximum principle of optimal control of stochastic delay equations on infinite horizon. We establish first and second sufficient stochastic maximum principles as well as necessary conditions for that problem. We illustrate our results with an application to the optimal consumption rate from an economic quantity.

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References

2005Applied Stochastic Control of Jump Diffusions 1997Backward stochastic differential equations and integral-partial differential equations 2006Backward stochastic differential equations with jumps and related non-linear expectations 2010Maximum principle for the stochastic optimal control problem with delay and application 2000Some Solvable Stochastic Control Problems With Delay 2000A maximum principle for optimal control of stochastic systems with delay, with applications to finance 2011Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations 2000Infinite horizon forward–backward stochastic differential equations

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2014Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach 2013Infinite horizon optimal control of forward–backward stochastic differential equations with delay 2013Maximum principles for jump diffusion processes with infinite horizon 2018Infinite horizon optimal control of mean-field forward–backward delayed systems with Poisson jumps

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