相关论文: Detection of two-sided alternatives in a Brownian …

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

A finite horizon variant of the quickest change detection problem is studied, in which the goal is to minimize a delay threshold (latency), under constraints on the probability of false alarm and the probability that the latency is…

This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…

We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged…

First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This modifies a formula by Perry et al (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for…

A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of…

We consider a mean-field optimal control problem for stochastic differential equations with delay driven by fractional Brownian motion with Hurst parameter greater than one half. Stochastic optimal control problems driven by fractional…

We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance \sigma^2 and mean \mu such that \sigma^2=a\mu, where a>0 is a known constant; the change is in \mu from…

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…

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 consider the offline change point detection and localization problem in the context of piecewise stationary networks, where the observable is a finite sequence of networks. We develop algorithms involving some suitably modified CUSUM…

The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: the underlying stochastic process has…

We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model…

Change in the coefficients or in the mean of the innovation distribution of an INAR(p) process is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of these quantities separately, or…

We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…

We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…

We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…

Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the…

This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…

In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval $(0,1)$ with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique…