SELF-SIMILAR PROCESSES AS WEAK LIMITS OF A RISK RESERVE
PROCESS
Abstract: Self-similar processes are closely connected with limit theorems for identical and in
general strongly dependent variables. Moreover, since they allow heavy-tailed distributions
and provide an additional “adjusting” parameter they appear to be interesting in the area
of risk models. In this paper we prove that only self-similar processes with stationary
increments appear naturally as weak limits of a risk reserve process, and conversely every
finite mean -self-similar process with stationary increments for can result as
the weak approximation. A lower bound for general self-similar processes with drift is also
provided.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -