On some minimax sequential decision problems with partial observability
Review: Jacek Koronacki, Jan Mielniczuk, Statystyka dla studentów kierunków technicznych i przyrodniczych
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Optimal stopping of a risk process
Optimal stopping time problems for a risk process where the number N(t) of losses up to time t is a general renewal process and the sequence of ’s represents successive losses are studied. N(t) and ’s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].
Modelling stock returns with AR-GARCH processes.
Financial returns are often modelled as autoregressive time series with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studied in financial and econometric literature as risk models of many financial time series. Analyzing two data sets of stock prices we try to fit AR(1) processes with GARCH or EGARCH errors to the log returns. Moreover, hyperbolic or generalized error distributions occur to be good models...
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