The paper presents an application of stochastic control methods to fixed income management in an incomplete market with external economic factors. The objective of an investor is the minimization of a shortfall risk. The problem is reduced to the multidimensional Bellman equation. It is shown that for a large class of loss functions the equation possesses a continuous solution. We also consider loss functions from the HARA class and prove that for such functions the Hamilton-Jacobi-Bellman equation...
There is a number of powerful software packages intended to solve numerical problems and differential equations in particular. First of all, we can mention here MATLAB, Maple and Mathematica. Recently to that list we can add R. The advantage of using R as compared to the previously mentioned programs, which are rather expensive, is that R is an open source software. At the same time, the recent development of R make it a very powerful and flexible software for solving differential equations. The...
This is a well-written survey paper on post-Heath-Jarrow-Morton interest rate models. The bond pricing and term structure are based on time-dependent continuous-time diffusions, and the main particular cases, including LIBOR and SWAP, are studied in detail.
"Applied mathematics" is mathematics, which is the subject of research relationships with reality out of mathematics (physical, biological, technical, economical ). The Polish world of mathematics also operates the term "application of mathematics" , which, despite another semantic significance is synonymous with the first . Both of these names correspond to one by English term "applied mathematics".
We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent')...
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