Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction Costs

Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction... Optimal stopping and impulse control problems with certain multiplicative functionals are considered. The stopping problems are solved by showing the unique existence of the solutions of relevant variational inequalities. However, since functions defining the multiplicative costs change the signs, some difficulties arise in solving the variational inequalities. Through gauge transformation we rewrite the variational inequalities in different forms with the obstacles which grow exponentially fast but with positive killing rates. Through the analysis of such variational inequalities we construct optimal stopping times for the problems. Then optimal strategies for impulse control problems on the infinite time horizon with multiplicative cost functionals are constructed from the solutions of the risk-sensitive variational inequalities of "ergodic type" as well. Application to optimal investment with fixed ratio transaction costs is also considered. Applied Mathematics and Optimization Springer Journals

Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction Costs

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Copyright © 2007 by Springer
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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