Use of Stochastic Asset-liability Model to Find Unique Price of Asset

Abstract

‘Asset–liability control’ is meant for managing the risk arising from changes in the relationship between assets and liabilities, due to volatile interest rate in critical situations like economic recession, inflation, etc. A stochastic asset-liability model (ALM), if adopted, and the market, though incomplete, is in equilibrium, a unique price can be obtained that is consistent both with the ALM and with the market. This paper presents a stochastic asset-liability model. A unique price, consistent with the ALM and the market, is obtained given a precise condition. The present market value of asset is also obtained with the given unique price. This classical problem considers an amount of money which an institution has in the bank that grows deterministically and a risky asset such as a stock whose value follows a geometric Brownian motion with a drift.