arXiv research

The paper studies risk-sensitive MDPs with recursive risk measures.

In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…

Study risk-sensitive reinforcement learning with entropic risk measures and generative models.

Framework for quantifying uncertainty in dynamic processes.

Paper estimates the order of vertices in random recursive trees.

Study dynamic Pareto-optimal allocations in multi-period economies with time-consistent risk measures.

We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal prediction, where at each stage the recursion depends on the whole future. The propert…

Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representat…

In this paper we present results on dynamic multivariate scalar risk measures, which arise in markets with transaction costs and systemic risk. Dual representations of such risk measures are presented. These are then used to obtain the main results of this paper on time consistency; namely, an equivalent recursive form…

The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be made in a basket of currencies or assets. Time consistency of scalar risk measu…

Dynamic risk measures follow law invariance principles over time.

A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a finite probability space. The set of capital requirements at each time and state is c…

The paper uses LSM to solve complex monetary utility functions.

Develops a new method for risk diversification using dynamic risk measures.

Estimate arrival times in random recursive trees using iterated Jordan centralities.

The paper studies optimal investment using acceptability indices to maximize portfolio performance.

Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.

Study optimizes insurance and investment strategies for risk-averse insurers under ambiguity.

We study multiple defaults where the global market information is modelled as progressive enlargement of filtrations. We shall provide a general pricing formula by establishing a relationship between the enlarged filtration and the reference default-free filtration in the random measure framework. On each default scena…

In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variabl…

New random forest algorithms for PU learning minimize risk directly.

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 risk is measured by variance) or more generally, the dynamic mean-risk problem. I…

The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a dual representation of dynamic cash-subadditive convex risk measures (that can al…

A Kalman filter reduces valuation risk in business valuation models.

This paper provides a methodology for fast and accurate pricing of the long-dated contracts that arise as the building blocks of insurance and pension fund agreements. It applies the recursive marginal quantization (RMQ) and joint recursive marginal quantization (JRMQ) algorithms outside the framework of traditional ri…

Paper presents a neural network method for efficient xVA computation and risk management.

Deep RL solves dynamic risk pricing for complex financial models.

New method improves credit risk estimation and pricing.

Estimates and optimizes UBSR risk in recursive settings.

Margin system for margin loans using cash and stock as collateral is considered in this paper, which is the line of defence for brokers against risk associated with margin trading. The conditional probability of negative return is used as risk measure, and a recursive algorithm is proposed to realize this measure under…

In order to protect brokers from customer defaults in a volatile market, an active margin system is proposed for the transactions of margin lending in China. The probability of negative return under the condition that collaterals are liquidated in a falling market is used to measure the risk associated with margin loan…

Paper analyzes time series prediction using empirical risk minimization.

We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Per…

The paper develops a new formula for financial pricing under multiple interest rates and collateralization.

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our propose…

Improved tail risk forecasting model for assets using CAViaR with spillover effects.

We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale approach and analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equatio…

This paper studies an optimal investment and risk control problem for an insurer with default contagion and regime-switching. The insurer in our model allocates his/her wealth across multi-name defaultable stocks and a riskless bond under regime-switching risk. Default events have an impact on the distress state of the…

Study uses reinforcement learning to optimize portfolios under recursive utility.

Improved real-time UAV terrain following with RVM-RLS filter.

In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$ under the assumption that the constant discount rate $ν\in (0,1)$. More specifical…

We first study an optimal stopping problem in which a player (an agent) uses a discrete stopping time in order to stop optimally a payoff process whose risk is evaluated by a (non-linear) $g$-expectation. We then consider a non-zero-sum game on discrete stopping times with two agents who aim at minimizing their respect…

New algorithm reduces prediction error in online learning without knowing base measure.

We develop recursive, data-driven, stochastic subgradient methods for optimizing a new, versatile, and application-driven class of convex risk measures, termed here as mean-semideviations, strictly generalizing the well-known and popular mean-upper-semideviation. We introduce the MESSAGEp algorithm, which is an efficie…

Recursive KalmanNet combines neural networks with Kalman filters for precise state estimation.

Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of computing both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro procedure based on Rockaffela…

We propose a general theory for constructing functorial assignments $Σ\longmapsto Ω_Σ \in E(Σ)$ for a large class of functors $E$ from a certain category of bordered surfaces to a suitable target category of topological vector spaces. The construction proceeds by successive excisions of homotopy classes of embedded pai…

Study risk-sensitive reinforcement learning with optimized certainty equivalents.