Related papers: Dynamic monetary risk measures for bounded discret…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
The aim of this work is to study risk measures generated by distortion functions in a dynamic discrete time setup, and to investigate the corresponding dynamic coherent acceptability indices (DCAIs) generated by families of such risk…
In normal times, it is assumed that financial institutions operating in non-overlapping sectors have complementary and distinct outcomes, typically reflected in mostly uncorrelated outcomes and asset returns. Such is the reasoning behind…
This paper presents an axiomatic scheme for interest rate models in discrete time. We take a pricing kernel approach, which builds in the arbitrage-free property and provides a link to equilibrium economics. We require that the pricing…
For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
In this paper, we investigate the problem of verifying the finite-time safety of continuous-time perturbed deterministic systems represented by ordinary differential equations in the presence of measurable disturbances. Given a finite-time…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation…
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has…
By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent…
In this paper we present a framework for risk-averse model predictive control (MPC) of linear systems affected by multiplicative uncertainty. Our key innovation is to consider time-consistent, dynamic risk metrics as objective functions to…
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which there are two risk-averse decision makers (i.e., {\it leader} and {\it follower}) with different risk-averse…
In this three-part series of papers, we argue that the conventional spread measures are not well defined for credit-risky bonds and introduce a set of credit term structures which correct for the biases associated with the strippable cash…
Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…