The price of portfolio selection under tail conditional expectation with consumption cost and transaction cost

Abstract

One of the ways of managing the risk that can arise from the changes in the relationship between assets and liabilities is by asset-liability management. Recently, Value-at-risk (VaR) and tail conditional expectation (TCE) have also emerged as standard tools for measuring and controlling the risk of trading portfolios. The limits of TCE can be transformed into the limits of VaR and conversely in some dynamical setting, TCE is preferable to VaR for being coherent. In this paper we obtain a portfolio selection model for an institution's assets- liabilities under the TCE with consumption cost and transaction cost. A set of partial dierential equations are derived and closed form solution proered, when there is no transaction cost.

Key words: Risk management; Tail conditional expectation; Asset-liability control; Value-at-risk; consumption cost; Transaction costs.