Jacques Janssen

Interaction between asset liability management and risk theory

In order to apply the ALM model of Janssen 1 (see also References 2 and 3), 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 4 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≥ 0) defined by a t = In(A t /B t ) and at the first mismatching time τ = inf{t: 0 ≤ t ≤ T, a(t) ≤ 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 5,6 and Sacerdote and Tomasetti. 7 A degree of mismatching follows from option theory. These results are important as they are useful to determine ALM-strategies for insurance companies.

Agricultural finance revenue futures contract

To respond to financial compound risk of farmers, two multiplicative derivative contracts, called respectively revenue futures contract and revenue put option, are proposed. The paper presents the theoretical management strategy of such a contract under the constraint that price and crop yield futures contracts are quoted. A financial intermediary can thus develop a risk-free management strategy to build a revenue futures contract. This paper opens perspectives on risk management for farmers, on completeness of markets and on new financial intermediation.