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Applications of variational inequalities in stochastic control
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The article was published on 1982-01-01 and is currently open access. It has received 465 citations till now. The article focuses on the topics: Obstacle problem & Variational inequality.read more
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Controlled diffusion processes
TL;DR: In this article, the authors give an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions.
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On the optimal stopping problem for one-dimensional diffusions
Savas Dayanik,Ioannis Karatzas +1 more
TL;DR: In this paper, a new characterization of excessive functions for arbitrary one-dimensional regular diffusion processes is provided, using the notion of concavity, and a new perspective and new facts about the principle of smooth-fit in the context of optimal stopping are presented.
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Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
TL;DR: In this paper, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets, and present and analyze multiscale stochastically volatility models and asymptotic approximations.
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Time reversal of diffusions
TL;DR: In this paper, it was shown that if a diffusion process on R^d satisfies a mild condition on drift and diffusion coefficient, then the density of the law of X_0 holds.
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A quantization tree method for pricing and hedging multidimensional american options
TL;DR: The quantization method is presented, which is well‐adapted for the pricing and hedging of American options on a basket of assets and results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids are provided.