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On Fractional Brownian Motion with Application to SMP: Risk Neutral & Sensitive Approaches
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This book extends Pontryagin's stochastic maximum principle to systems driven by fractional Brownian motion . It explores two main topics. The first deals with a risk-neutral optimal control problem, where the convex perturbation method is used to derive optimality conditions. The second topic focuses on risk-sensitive control, formulated via backward stochastic differential equation . Here, the goal is to minimize a convex disutility function of cost. The study links risk-neutral and risk-sensitive formulations, establishes the equivalence between exponential utility and quadratic BSDEs, and transforms the problem into a standard risk-neutral form to derive a stochastic maximum principle.
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This book extends Pontryagin's stochastic maximum principle to systems driven by fractional Brownian motion . It explores two main topics. The first deals with a risk-neutral optimal control problem, where the convex perturbation method is used to derive optimality conditions. The second topic focuses on risk-sensitive control, formulated via backward stochastic differential equation . Here, the goal is to minimize a convex disutility function of cost. The study links risk-neutral and risk-sensitive formulations, establishes the equivalence between exponential utility and quadratic BSDEs, and transforms the problem into a standard risk-neutral form to derive a stochastic maximum principle.
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