Some contributions to stochastic control and backward stochastic differential equations in finance.

Abstract : In my Phd thesis, I give some stochastic control approaches to some financial problems. In the first chapter, we consider a mixed investment-sell problem. This problem consist in studying the behavior of an agent who possesses one unit of an indivisible asset to be sold, and continuously trades on some given risky assets. In the second chapter, we study first order and second order BSDEs with convex constraints. In each case, we prove the existence of a minimal solution together with a stochastic representation formula for this problem. In the last chapter, we study a stochastic volatility model where the instantaneous volatility depends on the forward volatility curve. We give an asymptotic expansion for an option price for small variations of the volatility.
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Submitted on : Tuesday, May 22, 2012 - 2:32:01 PM
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Emilie Fabre. Some contributions to stochastic control and backward stochastic differential equations in finance.. Optimization and Control [math.OC]. Ecole Polytechnique X, 2012. English. ⟨pastel-00700157⟩

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