arXiv research

Study on implied certainty equivalent rates in financial markets and electric vehicles.

Solves Merton's investment-consumption problem with certainty equivalent approach.

Study shows certainty equivalent policy minimizes regret in continuous-time systems.

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very …

The paper develops a new approach to conditional risk measures using modular convex analysis.

The paper analyzes risk estimation methods and derives bounds for OCE risk.

New multivariate risk measures improve on univariate OCE methods.

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

Proposes a new method to rank risky investments based on Omega measure.

Study risk-sensitive market making with entropy regularization for better quote control.

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduc…

Deep learning solves dynamic programming with recursive utility.

Introduces new performance measures using scaled utility functions.

Study scaling limits for option pricing in trinomial models.

CEFOL uses deep learning for dynamic programming with recursive utility.

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

Study risk-sensitive reinforcement learning with optimized certainty equivalents.

This work uses a scalable approach to identify partially observed nonlinear systems.

Study optimal investment decisions for diverse risk-tolerant agents.

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectivel…

This paper shows CEM is a special case of TTM, leading to new proofs and improved sample complexity bounds.

We consider a model in which a trader aims to maximize expected risk-adjusted profit while trading a single security. In our model, each price change is a linear combination of observed factors, impact resulting from the trader's current and prior activity, and unpredictable random effects. The trader must learn coeffi…

We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and t…

This paper introduces new risk measures for evaluating losses with varying time horizons.

The paper develops robust risk measures for uncertain loss positions.

This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric Brownian motion and exponential Ornstein-Uhlenbeck models -- to account for, respectiv…

Submodularity is studied for convex risk measures, including Expected Shortfall.

New bounds for adaptive control in high dimensions without fixed state space.

Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk measures and average value at risk. In this work we consider stochastic optimal control…

This paper tackles adaptive control of unknown Markov jump systems with sample complexity and regret bounds.

New method for dynamic valuation in markets with random endowments.

We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as $\widetildeΘ({\sqrt{d_{\mathbf{u}}^2 d_{\mathbf{x}} T}})$, where $T$ is the number of time steps, $d_{\m…

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including t…

We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with ambiguity. We obtain the dynamic …

The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.

New findings reveal discount regularization can be seen as a strong prior, leading to poor performance in unevenly sampled data.

Investment strategy optimizes risk using a specific risk measure.

We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…

We consider the optimal investment problem when the traded asset may default, causing a jump in its price. For an investor with constant absolute risk aversion, we compute indifference prices for defaultable bonds, as well as a price for dynamic protection against default. For the latter problem, our work complements S…

We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical optimization. Through a computational study involving a stochastic version of a well …

Investors optimize equity and CDS trading to mitigate default risk.

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 representation for the solution of the optimal stopping problem. In particular, we …

Optimizes information acquisition to reduce estimation risk and maximize utility.

New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading …

This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the m…

Paper tackles anomaly detection in restless Markov arms with unknown TPMs.

We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather use historical stock prices and an a priory given distribution of the appreciati…

A new option pricing model handles non-constant risk aversion and transaction costs.