*Tid:***7 december 1998 kl 1615-1700**(OBS! Tiden)

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Mattias Andersson
**

**Titel:** **
Modelling long-term capital markets. (Examensarbete)
**

*Sammanfattning: *

This master thesis explores the modelling of capital markets in a long-term perspective. GARCH models for stochastic returns and volatilities are presented among with compensations for the time horizon. It turns out that autocorrelations in returns reduces the volatility of returns when the time horizon of these grows. This fact is compensated for using a model where each outcome of the random part of the returns process is dependent on the accumulated sum of these outcomes, which generates the desired mean-reverting effect in the returns series. With the model formulated and fitted, the focus is set on simulation of the market and the problem of finding optimal investment strategies when certain restrictions are set on the portfolio. A special case occures when the portfolio is underlying of a minimum guarantee return contract, as is the case in many life insurance companies. The problem of pricing such a contract, given a portfolio strategy, is solved by Monte Carlo simulation under a martingale measure.