Stochastic Models of Asset Valuation in Markets with Frictions

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ABSTRACT: The PI proposes to continue her program to develop methods to study abroad range of valuation problems in portfolio management and assetpricing. More precisely, using techniques from the theories of stochasticcontrol and nonlinear partial differential equations, the PI proposes tocontinue her research program in the following two general areas:A. Models with transaction costs: The goal is to investigate (i) thevaluation of early exercise instruments and exotic derivatives in amulti-security framework, (ii) the estimation of hedging probabilities ina relaxed super replication setting, (iii) the impact of a finite horizonto trading policies, and (iv) the asset valuation with transaction costsand alternative price processes.B. Models with stochastic volatility: The goals are (i) the completecharacterization and calibration of stochastic volatility functions and(ii) the analysis of delta hedging and value at risk in the presence ofstochastic volatility and unhedgable risks. Financial markets are not "perfect" due to the presence of variousfrictions like transaction costs, asymmetric information, stochasticvolatility, trading constraints, irreversibilities and liquidity. Thesemarket imperfections generate unhedgable risks which cannot be priced viathe existing classical valuation principles. This project proposes to introduce novel valuation methodologies and to analyze the relevantstochastic optimization problems. In addition to the areas of derivativepricing and portfolio management, it is expected that the new results willbe applied to other valuation systems arising in corporate finance, creditrisk, insurance theory, electronic commerce and optimal environmentalmanagement.