Dynamic programming approach to principal–agent problems

We consider a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically on the recent extensions to the second order case.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Portfolio Diversification Benefits at Different Investment Horizons During the Arab Uprisings: Turkish Perspectives Based on MGARCH–DCC and Wavelet Approaches

This study is an initial attempt at investigating the extent to which portfolio diversification benefits at different investment horizons are available to a Turkish investor from investment in MENA countries exposed to the Arab spring based on MGARCH-DCC and Wavelet techniques on daily data spanning from 2005 to 2015. The findings tend to suggest that the Turkish investors may not benefit from investment in Egypt for almost all investment horizons but may have moderate benefits from Lebanon up to the investment horizons of 32–64 days and longer. However, Turkish investors may benefit from Oman excepting the longer investment horizons. In the long run, all stock holding periods exceeding 32 days have minimal benefits for portfolio diversification.