Dynamic risk constraints help limit risky behavior in financial portfolios.
problem Static risk measures fail to control tail-risk-seeking traders.
method Introduces dynamic risk constraints applied throughout the trading horizon.
result Dynamic risk constraints can effectively limit risky behavior in portfolios.
This paper studies the problem of optimal investment with CRRA (constant, relative risk aversion) preferences, subject to dynamic risk constraints on trading strategies. The market model considered is continuous in time and incomplete. the prices of financial assets are modeled by Itô processes. The dynamic risk constr…
Optimizes multi-period portfolios with tail-risk constraints using neural networks.
problem Maximizing expected return while managing tail-risk constraints over multiple periods.
method Recurrent neural network approach to approximate optimal policy.
result Validated in financial and insurance models, capturing long-term risk dynamics.
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss i…
Framework for controlling multiple risks in AI models.
problem Enforcing multiple risk constraints in generative AI models.
method Formalizes problem, introduces two dynamic programming algorithms.
result Achieves nearly tight control of all constraint risks under mild assumptions.
Deep Hedging learns risk-neutral vol dynamics for option pricing.
problem Statistical arbitrage in market dynamics without transaction costs.
method Numerical approach to train market simulator and find risk-neutral density.
result Risk-neutral model for stochastic implied volatility can be used for pricing or Deep Hedging.
New method separates model and non-model risks for more practical asset pricing.
problem Asset pricing under model-uncertainty.
method Binary model-risks and constraints over preferences; unique model-risk pricing formula.
result Unique model-risk pricing formula with dynamically conserved constant.
This paper characterizes the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints and found to match real world observations about financi…
Dynamic reinsurance aims to minimize surplus risk using martingale transport.
problem Minimizing surplus risk in dynamic reinsurance.
method Martingale optimal transport techniques.
result A tractable solution analogous to the Bass martingale is found.
Neural SDEs model suicide risk with compact state space constraints.
problem Modeling suicide risk with irregular, noisy, and partially observed data.
method Developed neural SDEs confined to compact state spaces, addressing domain constraints and numerical stability.
result Improved forecasts and optimization dynamics over standard models on EMA datasets.
The paper optimizes pension policies with guarantees and sustainability constraints.
problem Designing optimal pension policies with guarantees and sustainability constraints.
method Dynamic utility model, stochastic domain, overlapping generations, time-consistent decision criterion.
result Optimal investment/pension policy computed for a general framework.
Dynamic tracking error framework shows similar performance but varying volatility across different constraints.
problem Differences in governance parameters between Total Portfolio Approach and Strategic Asset Allocation.
method Portfolio simulations using U.S. equity and bond data from 2000 to 2026, spanning 2004 to 2026.
result Realized tracking error volatility varies 12-fold across different constraints, with costs highest during crises.
Solves portfolio optimization with costs using numerical methods.
problem Dynamic portfolio optimization with transaction costs and constraints.
method Numerical dynamic programming techniques.
result Problems can now be solved tractably.
Study risk-averse insider's behavior in dynamic signal asset pricing.
problem Analyzing risk-averse insider's dynamic signal in asset pricing.
method Employing a weak conditioning methodology to construct a Schrödinger bridge, deriving necessary conditions for equilibrium.
result Derive explicit closed-form solutions for important cases.
A new RL method handles uncertainty and constraints in real-time optimization.
problem Real-time optimization under process uncertainty and constraints.
method Chance-constrained reinforcement learning to handle probabilistic state constraints.
result Satisfies process constraints with high probability in real-time.
Paper uses DRL to optimize portfolios, balancing risk and return.
problem Optimizing portfolios under market uncertainty and risk constraints.
method Integrates Sharpe ratio-based reward with risk control mechanisms, uses PPO for adaptive asset allocation.
result DRL agent stabilizes volatility but sacrifices risk-adjusted returns.
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimalit…
Study a continuous portfolio optimization with a new CVaR-like constraint using martingale approach.
problem Optimizing a portfolio under a new CVaR-like constraint that is not compatible with traditional methods.
method Follows a martingale approach in a complete market setting, solving a convex constrained minimization problem.
result Obtains a tractable and interpretable characterization of the optimal strategy.
New method optimizes portfolios by dynamically integrating ESG constraints.
problem Static ESG scores mismatch sequential portfolio decisions.
method MACF-X, a family of adapters that learns ESG costs from multimodal evidence.
result Reduces tail ESG budget pressure while maintaining financial performance.
Study dynamic risk measures with distributional uncertainty using optimal transport.
problem Risk robustification under distributional uncertainty in Markovian models.
method Characterize risk measures via convex monotone semigroups and optimal transport costs.
result Identify generator and correction terms for dynamic risk measures under different scaling regimes.
The 2008 mortgage crisis is an example of an extreme event. Extreme value theory tries to estimate such tail risks. Modern finance practitioners prefer Expected Shortfall based risk metrics (which capture tail risk) over traditional approaches like volatility or even Value-at-Risk. This paper provides a quantum anneali…
A new approach optimizes weights in DLP for better risk-adjusted performance.
problem Optimizing time-varying weights in Double Linear Policy (DLP) for better risk-adjusted performance.
method Stochastic Model Predictive Control (SMPC) framework to maximize risk-adjusted returns while enforcing constraints.
result Empirical results show improved risk-adjusted performance and drawdown control.
We present a simple agent-based model of a financial system composed of leveraged investors such as banks that invest in stocks and manage their risk using a Value-at-Risk constraint, based on historical observations of asset prices. The Value-at-Risk constraint implies that when perceived risk is low, leverage is high…
Dynamic model considers private asset markets' complexities.
problem Understanding and optimizing private asset allocation.
method State-of-the-art dynamic model with machine learning.
result Optimal investment policies quantified over fund life.
The study tests a functional-form restriction on risk exposure dynamics using margin debt data.
problem Understanding risk exposure dynamics under capital constraints and slack.
method Testing a regime-conditional functional-form restriction on aggregate risk-exposure dynamics implied by VaR-constrained intermediary models.
result The contraction and growth of exposures under capital constraints and slack are observed and tested.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
Study risk aggregation with order constraint under unknown dependence.
problem Risk aggregation with an order constraint under uncertainty.
method Introduced DL coupling for concave order risk aggregation, generalized to tail risk measures.
result Analytical formulas for bounds on Value-at-Risk with improved accuracy.
Solves VaR-constrained portfolio optimization in markets with stochastic volatility.
problem Optimizing portfolio in markets with stochastic volatility under VaR constraints.
method Dynamic programming approach to Heston's stochastic volatility model.
result Optimal investment strategy linked to unconstrained problem via a vega-neutral derivative.
Study shows equivalence of four risk constraints in non-concave optimization problems.
problem Investigating risk constraints in non-concave optimization for financial companies.
method Analytical solutions for four risk constraints (ES, EDS, VaR, AVaR) under non-concave optimization.
result All four risk constraints lead to the same optimal solution, differing from concave optimization.
The study analyzes ETFs' portfolio optimization and tail-risk management.
problem Analyzing the performance of actively managed ETFs in managing risk and diversification.
method Daily Bloomberg data for 30 funds, evaluating various strategies under long-only and long-short constraints.
result Tangency-type portfolios generally outperform buy-and-hold benchmarks, while minimum-variance and CVaR-minimizing portfolios sacrifice upside for downside control.
Neural nets optimize dynamic hedging strategies with transaction costs.
problem Optimal hedging strategy in presence of transaction costs and discrete time.
method Convolutional neural network trained to infer optimal hedging frequencies.
result Dynamic multiscale hedging strategy reduces risk and maximizes profit.
This paper uses entropy to derive stock price dynamics and option valuation.
problem Deriving stock price dynamics and option valuation from information constraints.
method Develops an entropic inference framework to derive stochastic processes from information constraints, representing price changes through two channels: continuous and jump.
result The derived dynamics is the Merton jump diffusion, with Geometric Brownian Motion as the no jump limit.
Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton …
In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is i…
Comonotonic allocations are restored under certain constraints, improving risk-sharing.
problem Feasibility constraints can distort optimal risk-sharing allocations.
method Identified componentwise convex-order solidity as a sufficient condition to restore comonotonic allocations.
result Componentwise convex-order solidity ensures comonotonic improvements under feasible constraints.
Model predicts insolvency risks in banks due to liquidity and credit risks.
problem Determining insolvency regions in banks due to non-linear interaction between liquidity and credit risks.
method Developed a continuous-time structural dynamic model integrating Basel III requirements into a stochastic optimal control framework. Used Hamilton-Jacobi-Bellman (HJB) equation to solve for insolvency boundary. Derived surrogate analytical approximation for real-time monitoring.
result Calibrated model reveals significant non-linear threshold effects and accelerates insolvency transition.
Reinsurance can help life insurers maintain higher capital guarantees without losing utility.
problem Decreasing capital guarantees in life insurance products.
method Dynamic investment-reinsurance optimization problem with simultaneous Value-at-Risk and no-short-selling constraints. Introduced guarantee-equivalent utility gain for comparison.
result Optimally managed reinsurance allows insurers to offer higher capital guarantees without reducing expected utility.
Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of Neyman-Pearson type binary solution. We add a constraint on expected return to investigate the Mean-CVaR portfolio sele…
The dynamic network of relationships among corporations underlies cascading economic failures including the current economic crisis, and can be inferred from correlations in market value fluctuations. We analyze the time dependence of the network of correlations to reveal the changing relationships among the financial,…
We propose a unified structural credit risk model incorporating both insolvency and illiquidity risks, in order to investigate how a firm's default probability depends on the liquidity risk associated with its financing structure. We assume the firm finances its risky assets by mainly issuing short- and long-term debt.…
Proposes a reverse stress testing framework for dynamic models.
problem Finding plausible models under adverse stresses.
method Compound Poisson process, Kullback-Leibler divergence, optimization problem.
result Intensity and severity of process depend on time and state.
Paper studies optimal investing for retirees with risk constraints.
problem Retirees' longevity and living standard risks in a fluctuating market.
method Formulated as a portfolio choice problem under time-varying risk capacity constraint. Derived optimal investment strategy using differential equations. Demonstrated endogenous spending measure and active investment strategy.
result Time-varying risk capacity constraint impacts asset allocation in retirement.
Study optimizes portfolio allocation policies using off-policy data and constraints.
problem Optimizing portfolio allocation policies under constraints using off-policy data.
method Solves a minimax objective with off-policy estimators and online learning to control constraint violations.
result Constructs near-optimal allocation policies for various regimes of operation and constraints.
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether such ρ-ar…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading strategy in risky assets …
A risk-neutral method is always used to price and hedge contingent claims in complete market, but another method based on utility maximization or risk minimization is wildly used in more general case. One can find all kinds of special risk measure in literature. In this paper, instead of using market modified risk meas…
In this work we consider adversarial contextual bandits with risk constraints. At each round, nature prepares a context, a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and then receives the corresponding cost and risk associated with the pulled arm. In additi…
Paper proposes a risk-aware decision-making framework for real-world sequential decisions.
problem Real-world sequential decision-making problems often have critical constraints that learning solutions often neglect.
method Actor multi-critic architecture with risk characterization.
result Our approach consistently satisfies system constraints with minimal performance toll.