Interaction between asset liability management and risk theory

Interaction between asset liability management and risk theory

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Article ID: iaor2000242
Country: United States
Volume: 14
Issue: 4
Start Page Number: 295
End Page Number: 307
Publication Date: Dec 1998
Journal: Applied Stochastic Models and Data Analysis
Authors: ,
Keywords: insurance, asset liability management
Abstract:

In order to apply the asset liability management (ALM) model of Janssen to insurance companies, we study an extension of the model in which the asset fund A takes into account fixed-income securities. Therefore, we model the rates of return of the portfolio by a Vasicek process. The liability process B is defined by a geometric Brownian motion with drift which may be correlated with the asset process. In this generalized Janssen model we concentrate on the relations between the asset process A and the liability process B in order to point out some management principles. More exactly, we study the probability that the assets and liabilities of a company have no good matching and we propose some indicators of the mismatching. Therefore, we look at the process a = (a(t), t greater than or equal to 0) defined by a = ln(A(t)/B − t) and at the first mismatching time τ = inf{t:0 less than or equal to t less than or equal to T, a(t) less than or equal to 0}. The determination of the probability of mismatching leads to the calculation of crossing probabilities P[τ < T]. Only in special cases, explicit results are obtained and we turn for the general cases to the approximations proposed by Durbin and Sacerdote and Tomasetti. A degree of mismatching follows from option theory. These results are important as they are useful to determine ALM-strategies for insurance companies.

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