On Lower Partial Moments for an Investment Portfolio With Variance-Gamma Distributed Returns

Abstract

The paper discusses the lower partial moments for the return of the investment portfolio which consists of the assets whose random incomes are modeled by variance-gamma, gamma distributions and constants.

The formulas depend on values of generalized hypergeometric functions. As a corollary, the target semideviation is computed.

It is shown also how the obtained results generate analytical expressions for the value at risk and the expected shortfall monetary risk measures.

Keywords: lower partial moment, semideviation, variance-gamma distribution; generalized hypergeometric function; value at risk; expected shortfall

JEL Classification: C02; C63; G11; G21; G32