Optimal stopping in models with random observations

Prelegent(ci)

Svetlana Boyarchenko

Afiliacja

The University of Texas at Austin, USA

Język referatu

angielski

Termin

11 grudnia 2024 14:15

Pokój

p. 5070

Seminarium

Seminarium Zakładu Biomatematyki i Teorii Gier

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Quantifying risks related to events that arrive at random times, along with the frequency of their arrivals, is crucial in fields such as finance, insurance, cybersecurity, and disaster management. The standard assumption in the literature is that events such as breakthrough innovations or breakdowns in machinery arrive at jump times of the Poisson process with a random hazard rate. Popular Poisson bandits models postulate that the hazard rate can take only two values, say 0 \leq lambda_1 < lambda_2.  These models impose an upper bound lambda_2 on the frequency of arrivals which is not always reasonable. They are not suitable to study long-term effects of experimentation because the hazard rate of the standard Poisson process is constant. The settings of these models also disregards that costs or profits the risky endeavor can be stochastic. I demonstrate how introducing more realistic features into the standard experimentation models can change optimal stopping decisions, including safety standards in testing products that may possess harmful qualities. I also introduce a relatively simple theoretical model of learning and decision making under uncertainty generated by a Poisson process of stochastic intensity. The prior distribution for the random intensity  is the gamma distribution. I suggest a new type of decision rules which I call the two-clock decision making. One clock measures the calendar time. The second clock - a discrete one - measures how many events of interest were observed since the beginning of experimentation.

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