Jared Ackley

Document Type

Honors Thesis


Consider a sequence of independent and identically distributed random variables Zi, i = 1,2,... and an integer-valued random number M with a log-concave pmf that is independent of Zi, = 1,2,. It is known that Sy = Le1 Z; is log-concave. This can be applied to the classical Lundberg risk model by choosing Z; to be record lows and M to be a geometric random variable representing the total number of record lows. Choosing L to be the sum of the random number of record lows, it was found that 1 (u) = P(L ≤ u) is a log-concave function of the initial capital u. Given N risk processes with initial capitals U¡, i = 1,2, ..., N satisfying U El U;, Lagrange multipliers were used to determine optimal capitals that maximize the probability of no risk process running out of money. Numerical calculations in the case of N = 2 were carried out and analyzed.

Publication Date






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