Arbitrage and sampling uncertainty in financial stochastic programming models

A.B. Berkelaar, H. Hoek and André Lucas ()

No EI 9919-/A, Econometric Institute Report from Erasmus University Rotterdam, Econometric Institute

Abstract: Asset liability management (ALM) is an important and challengingproblem for institutional investors and financial intermediaries. Therequirement to fulfill its liablilities constrains the institutionalinvestor in its asset allocation possiblilites. We formulate an ALMmodel for pension funds as a multistage stochastic programming model.Relevant variables such as future inflation rates, stock retruns, andbond yields are unknown. This is incorporated in the ALM model bymeans of an event tree, which represents the expected development ofthe economic variables as well as the corresponding uncertainty. The event tree is constructed by sampling from a time series modelfor the variables, and is therefore subject to sampling uncertainty.Moreover, for the event tree to be realistic, it is required not toexhibit arbitrage opportunies. In ths paper we examine the effectof sampling uncertainty and the structure of the event tree on theoptimal policies. Furthermore, we consider the effect of randomsampling and the tree structure on the probability of arbitragefreetrees. We also compare the optimal solutions to the ALM problem fortrees with an without arbitrage. For these purposes, we considerdata from a Dutch pension fund.

Keywords: stochastic programming; asset liability management (search for similar items in EconPapers)
Date: 1999-04-26
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:eureir:1765001589

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