We review an emerging application field to parabolic partial differential equa- tions (PDEs), that’s economic growth theory. After a short presentation of con- crete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In...

We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an appropriate rescaling of the time parameter, the empirical...

This study presents numerical schemes for solving two three-dimensional parabolic inverse problems. These schemes are developed for indentifying the parameter p(t) which satisfy ut=uxx+uyy+uzz+p(t)u+φ, in R×(0,T], u(x,y,z,0)=f(x,y,z),(x,y,z)∈R=[0,1]3. It is assumed that u is known on the...

As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to...