Optimization Methods in Mathematical Finance

Optimization Methods in Finance

Problems for ’Mathematical methods in finance’

(non strict second order dominance) iff Eu(A) ≥ Eu(B) for all utility functions u on [a, b] such that u′ ≥ 0 and u′′ ≤ 0 . 3. Second order dominance and stop loss. Show that (1) holds (i) iff E(B−d)− ≥ E(A− d)− for all d ∈ [a, b] or (ii) iff Emin(d,B) ≤ Emin(d,A) for all d ∈ [a, b]. 4. Utility and ARA. (a) Show that there exists a unique utility function u on R with a given ARA ρ(x) and such th...

Topics in Mathematical Finance Topics in Mathematical Finance

A Dissertation submitted for the Degree of Doctor of Philosophy To the memory of my mother Contents Preface iii 1 Introduction 1 1.1 Option pricing in discrete time 1 1.2 Option pricing in continuous time 4 1.3 The Black-Scholes model 8 1.4 Interest-rate models 9

Duality and optimality conditions in stochastic optimization and mathematical finance

This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations research and mathematical finance. The second part derives optimality conditions by combining general saddle-point conditions from convex duality with the dual repr...

Convex Duality in Stochastic Optimization and Mathematical Finance

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of prob...