Stochastic Analysis with Financial Applications

Part I: Stochastic Analysis.- Dirichlet forms for Poisson measures and Lévy processes: the lent particle method.- Backward stochastic difference equations with finite states.- On a forward-backward stochastic system associated to the Burgers equation.- Quantifying model uncertainties in complex systems.- On the estimate for commutators in DiPerna-Lions theory.- Approximation theorem for stochastic differential equations driven by G-Brownian motion.- Stochastic flows for nonlinear SPDEs driven by linear multiplicative space-time white noises.- Optimal stopping problem associated with jump-diffusion processes.- A review of recent results on approximation of solutions of stochastic differential equations.- Strong consistency of Bayesian estimator under discrete observations and unknown transition density.- Stability of a nonlinear equation related to a spatially-inhomogeneous branching process.- Exponentially stable stationary solutions for delay stochastic evolution equations.- Robust stochastic control and equivalent martingale measures.- Multivalued stochastic differential questions driven by point processes.- Logarithmic derivatives of densities for jump processes.- Part II: Financial Applications.- Convertible bonds in a defaultable diffusion model.- A geometric approach to option pricing with transaction costs in discrete models.- Completeness and hedging in a Lévy bond market.- Asymptotically efficient discrete hedging.- Estimating joint default probability by efficient importance sampling with applications from bottom up.- Market models of forward CDS spreads.- Optimal threshold dividend strategies under the compound Poisson model with regime switching.