On Stochastic Optimization Problems and an Application in Finance
by Josef Anton Strini (Author)

About the author
Josef Anton Strini wrote his master’s thesis under the supervision of Prof. Dr. Stefan Thonhauser at the Institute of Statistics at Graz University of Technology, Austria.

About this book
Josef Anton Strini analyzes a special stochastic optimal control problem. The problem under study arose from a dynamic cash management model in finance, where decisions about the dividend and financing policies of a firm have to be made. Additionally, using the dynamic programming approach, he extends the present discourse by the formal derivation of the Hamilton-Jacobi-Bellman equation and by examining the verification step carefully. Finally, the treatment is completed by solving the problem numerically.

Brief contents
1. Preliminaries 1
    1.1. Introduction 1
    1.2. Markov processes 2
        1.2.1. Diffusion processes 11
        1.2.2. Compound Poisson processes 21
    1.3. Optimal control of Markov processes 22
        1.3.1. Dynamic programming 24
        1.3.2. Verification step 28
2. A singular stochastic control problem 35
    2.1. Introduction 35
    2.2. Model assumptions 36
    2.3. Singular stochastic control theory 41
        2.3.1. The infinite time horizon problem for Markov diffusions in Rd 42
        2.3.2. The singular stochastic control case 46
3. Establishing the solution 53
    3.1. Dynamic programming approach 55
        3.1.1. First step: The Hamilton-Jacobi-Bellman equation 56
        3.1.2. Second step: HJB solutions exceed the value function 61
        3.1.3. Third step: The conjectured optimal policy 72
        3.1.4. Fourth step: Optimality of the conjectured solution 88
    3.2. Resulting consequences and outlook 93
A. Numerical complement 95
Bibliography 105

Series: BestMasters
Pages: 116 pages
Publisher: Springer Spektrum; 1st ed. 2019 edition (March 7, 2019)
Language: English
ISBN-10: 3658256907
ISBN-13: 978-3658256906