Related papers: On a connection between total positivity and Berno…
The probability that a user will click a search result depends both on its relevance and its position on the results page. The position based model explains this behavior by ascribing to every item an attraction probability, and to every…
We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions…
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
We formalize the problem of maximizing the mean-payoff value with high probability while satisfying a parity objective in a Markov decision process (MDP) with unknown probabilistic transition function and unknown reward function. Assuming…
This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…
For a family of probability functions (or a probability kernel), cross modality occurs when every likelihood maximum matches a mode of the distribution. This implies existence of simultaneous maxima on the modal ridge of the family. The…
We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation. We show…
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…
Deciding the positivity of a sequence defined by a linear recurrence and initial conditions is, in general, a hard problem. When the coefficients of the recurrences are constants, decidability has only been proven up to order 5. The…
This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
Although average gain optimality is a commonly adopted performance measure in Markov Decision Processes (MDPs), it is often too asymptotic. Further incorporating measures of immediate losses leads to the hierarchy of bias optimalities, all…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when…
The impetus for writing this paper are the well publicized media reports that software failure was the cause of the two recent mishaps of the Boeing 737 Max aircraft. The problem considered here though, is a specific one, in the sense that…
We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite potential. The reaction term involves competing nonlinearities. More precisely, it is the sum of a parametric sublinear (concave) term and a…
Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is…
Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\sim \mathcal{D}(a_0,...,a_d),$ such that $\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\sum_{i=0}^da_i$ and such that $Y\sim \beta(1,a).$ We…