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Dear All,currently, I am trying to model the ALM-problem of a pension fund using stochastic control methods. The special assumption I make is that the utility function of the pension fund has a "kink" at the minimum funding level. At this point the utility function is continuous but not differentiable.Here is my question:1. Is anybody aware of articles dealing with portfolio optimization and utility functions with "kinks"?2. Can anybody recommend a good introduction to numerical solutions of the Hamilton-Jacobi-Bellmann equation based on finite-difference methods?Thanks a lot,Costica.

It sounds like you've formulated the problem already. It may help us if you write the equation here.P

Costica,I can't help with (1), but for (2), a good place to start is "Applied Computational Economics and Finance" by Miranda & Fackler -- its forthcoming from MIT press, but you can get the latest (approx 3-4 sigma complete) draft from here. It is written for Matlab, and there is a free toolbox that accompanies the text for solving Bellman problems.HTH,matt.

Costica:Mathematically, one takes a smooth function (when eps>0) which becomes kinked at eps = 0; if your problem is like I think it is, one finds the classic type results except that the optimal solution can be at the kink for a range of conditions (ie, one gets hung up in the kink, which I guess is different than having a kinky hang-up

Matt,thank you very much for the great link.Paul,Unfortunately I haven't formulated the problem yet... I will probably try to define the utility function piecewise and make sure there are no discontinuities.costica.

Hi,Prof. Harold Kushner is the standard reference for numericalsolutions of HJB-equation. He wrote a book about this issue:"Numerical Methods for Stochastic Control Problems in Continuous Time Harold Kushner (with P. Dupuis), Springer, 1992 (2nd ed. 2000)"I tried it myself. From my experience, you always have to limitthe control variable so that Grid works.http://www.dam.brown.edu/lcds/people/Kushner.htmlKeanu