In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (...
Determination of an appropriate warranty length for the lifetime of the product is an important issue to the manufacturer. In this article, optimal warranty length of the product for the combined free replacement and the pro-rata warranty policy is c...
This paper is concerned with a class of time-optimal control problems for the swing and the ski. We first consider the motion of a man standing on a swing. For simplicity, we neglect friction and air resistance and assume that the mass of the swing...
We demonstrate how a static optimal income taxation problem can be analyzed using dynamical methods. Specifically, we show that the taxation problem is intimately connected to the heat equation. Our first result is a new property of the optimal tax w...
A novel continuous-aperture-array (CAPA)-aided integrated sensing and communication (ISAC) framework is proposed. Specifically, an optimal continuous ISAC waveform is designed to form a directive beampattern for multi-target sensing while suppressing...
The optimal beamforming design for multi-user continuous aperture array (CAPA) systems is proposed. In contrast to conventional spatially discrete array (SPDA), the beamformer for CAPA is a continuous function rather than a discrete vector or matrix,...
This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are insufficient f...
We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state, discrete-time plants. The problem class includes entry-(exit-)time problems as well as minimu...
We describe the solution of an optimal stopping problem for a stable Lévy process killed at state-dependent rate, which can be seen as a model for bankruptcy. The killing rate is chosen in such a way that the killed process remains self-similar, and...
We propose a quantum algorithm for the purification of a generic mixed state $ρ$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number o...
The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite...
With the rapid growth in the fashion e-commerce industry, it is becoming extremely challenging for the E-tailers to set an optimal price point for all the products on the platform. By establishing an optimal price point, they can maximize overall rev...
The repair problem in distributed storage addresses recovery of the data encoded using an erasure code, for instance, a Reed-Solomon (RS) code. We consider the problem of repairing a single node or multiple nodes in RS-coded storage systems using the...
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There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of t...
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected ex...
In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary knowledge abo...
The individualized treatment rule (ITR), which recommends an optimal treatment based on individual characteristics, has drawn considerable interest from many areas such as precision medicine, personalized education, and personalized marketing. Existi...
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the cond...
We present an introduction to the field of statistical optimal transport, based on lectures given at École d'Été de Probabilités de Saint-Flour XLIX....