Investment strategies and compensation of a mean–variance optimizing fund manager

Abstract

This paper introduces a general continuous-time mathematical framework for solution of dynamic mean-variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean-variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme's symmetry on trading behaviour and fund performance.

An HJB Approach to a General Continuous-Time Mean-Variance Stochastic Control Problem

“…The Proof follows the same line of reasoning as in [2][Theorem 2.2] and making use of the definition for the function g. For part (i), it is straightforward to prove convexity, which implies continuity with respect to ψ. It is clear from the definition of V, V ε that they are decreasing in ψ for non-negative f, Φ.…”

“…This implies that the conditions for maximum can only be satisfied in the interval [ψ min , ψ max ]. We skip further details and refer the reader to [2] …”

“…Solutions in the spaces of functions with generalised derivatives (henceforth called Sobolev spaces) are obtained through reqularisation. A further extension of this method is presented in [2] where the viscosity solutions approach is followed. In the latter, each of the functionals either depending on the terminal value of the controlled process or on the integral from time 0 to time T of the controlled process are considered but separately.…”

“…With regards to the functional, the problem without a"final payment" Φ has been discussed in [1] with solutions in Sobolev spaces and the problems with either only integral functional or only "final payment" were discussed in [2] using Viscosity solutions. It is clear, however, that the solution to problem (2) cannot be derived as a combination of the previous two cases due to the supremum involved.…”

Kompensasi Dan Kepuasan Kerja Untuk Meningkatkan Kinerja Guru

“…Sisi organisasi kompensasi merupakan biaya yang harus dikeluarkan utnuk meningkatkan produktivitas ataupun kemampuan karyawannya (Gerhart, Minkoff, & Olsen, 1995).Jumlah kompensasi tergantungpada evolusi pasar, strategi, mengimplementasikandan kontrakkompensasi yang disepakati antara investor dan manajer. (Georgios Aivaliotis, (2014) ). Menurut (Sukamti, 1989)kompensasi merupakan balas jasa yang diberikan oleh organisasi/ perusahaan kepada karyawan, yang dapat bersifat financial maupun non finansial, pada periode yang tetap.…”