Nonlinear Valuation in Theory and Practice
Thursday, June 14, 2018 - 9:00am - 9:50am
Theoretically equilibrium possibilities may be expanded by reducing the number of critical states. Furthermore, nonlinear valuation procedures may be used to assist the attainment of an expanded equilibrium with fewer securities than even the number of critical states. Practically, risk is an exposure to change in value or the variation in value. The variation is described by the arrival rates of a bilateral gamma process distinguishing both the drift and volatility of upwards moves from their downward counterparts. Nonlinear valuation solves a nonlinear backward stochastic integro-differential equation that distorts downward the arrival rates of gains while simultaneously raising the arrival rates of losses. Solutions are illustrated for equity valuation that is contrasted with the computations for regulatory capital requirements.