APPLIED STOCHASTIC CONTROL OF JUMP DIFFUSIONS

By D. JOONO

CONTENTS STOCHASTIC CALCULUS WITH JUMP DI?USIONS BASIC DE?NITIONS AND RESULTS ON L´EVY PROCESSES THE ITˆO FORMULA AND RELATED RESULTS L´EVY STOCHASTIC DI?ERENTIAL EQUATIONS THE GIRSANOV THEOREM AND APPLICATIONS APPLICATION TO ?NANCE EXERCISES OPTIMAL STOPPING OF JUMP DI?USIONS A GENERAL FORMULATION AND A VERI?CATION THEOREM APPLICATIONS AND EXAMPLES STOCHASTIC CONTROL OF JUMP DI?USIONS DYNAMIC PROGRAMMING THE MAXIMUM PRINCIPLE COMBINED OPTIMAL STOPPING AND STOCHASTIC CONTROL OF JUMP DI?USIONS INTRODUCTION A GENERAL MATHEMATICAL FORMULATION APPLICATIONS SINGULAR CONTROL FOR JUMP DI?USIONS AN ILLUSTRATING EXAMPLE A GENERAL FORMULATION APPLICATION TO PORTFOLIO OPTIMIZATION WITH TRANSACTION COSTS IMPULSE CONTROL OF JUMP DI?USIONS EXAMPLES EXERCICES APPROXIMATING IMPULSE CONTROL OF DI?USIONS BY ITERATED OPTIMAL STOPPING ITERATIVE SCHEME COMBINED STOCHASTIC CONTROL AND IMPULSE CONTROL OF JUMP DI?USIONS A VERI?CATION THEOREM ITERATIVE METHODS VISCOSITY SOLUTIONS VISCOSITY SOLUTIONS OF VARIATIONAL INEQUALITIES THE VALUE FUNCTION IS NOT ALWAYS C1 VISCOSITY SOLUTIONS OF HJBQVI NUMERICAL ANALYSIS OF HJBQVI SOLUTIONS OF SELECTED EXERCISES 10 1 EXERCISES OF CHAPTER 1 10 2 EXERCISES OF CHAPTER 2 10 3 EXERCISES OF CHAPTER 3 10 4 EXERCISES OF CHAPTER 4 10 5 EXERCISES OF CHAPTER 5 10 6 EXERCISES OF CHAPTER 6 10 7 EXERCISES OF CHAPTER 7 10 8 EXERCISES OF CHAPTER 8 10 9 EXERCISES OF CHAPTER 9 REFERENCES