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Abstract. The American put option exercise boundary has been studied extensively as a function of time and the underlying asset price. In this paper we analyze its dependence on the volatility, since the Black and Scholes model is used in practice via the (varying) implied volatility parameter....
Abstract. In this paper we consider a nonlinear filtering problem with an unbounded observation coefficient, correlated noises, and a signal process driven by an infinite dimensional Brownian motion. We prove that the unnormalized filter admits a smooth density which is in the Schwartz space and...
Abstract. We consider an interacting system of n diffusion processes X n j (t): t∈[0,1] , j=1,2,. . ., n , taking values in a conuclear space Φ' . Let ζ n t =(1/n)Σ n j=1 δ Xnj(t) be the empirical process. It has been proved that ζ n , as n→∞ , converges to a deterministic measure-valued process...
Abstract. The uniqueness theorem for generalized solutions of initial-boundary problems for the Marguerre—Vlasov vibrations of shallow shells with clamped boundary conditions is proved. A unique method developed by the author, based upon a nonstandard treatment of smoothing operators, is applied...
Abstract. This paper develops a continuous time portfolio optimization model where the mean returns of individual securities or asset categories are explicitly affected by underlying economic factors such as dividend yields, a firm's return on equity, interest rates, and unemployment rates. In...
Abstract. An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential Riccati equation is studied from...
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