Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.
A neural network method improves CVA computations for complex financial portfolios.
problem Improving accuracy of CVA computations for large, diverse portfolios of financial derivatives.
method Proposes a neural network-based approach to adjust exercise strategies for counterparty default risk.
result Shows significant overestimation of CVA by standard methods, especially for non-extreme cases.
Analyzes robust portfolio optimization with multi-factor stochastic volatility.
problem Optimizing portfolios under uncertainty and volatility risks.
method Analytical derivation of optimal strategy under worst-case scenarios, comparison with strategies ignoring uncertainty, and numerical experiments.
result Effects of ambiguity and derivative trading on optimal portfolio selection.
Study on risk contributions of portfolios using lambda quantile risk measures.
problem No known allocation rule for non-positively homogeneous risk measures.
method Defined lambda quantiles on portfolio compositions, derived derivatives, and introduced generalized Euler contributions.
result Explicit formulae for the derivatives of lambda quantiles, showing their homogeneity properties.
Paper proves equivalences in portfolio optimization with new risk measures.
problem Portfolio optimization with novel risk measures.
method Derive subgradients and gradients for negative expectile and omega ratio.
result Negative expectile can be used as a portfolio optimization objective.
A new method uses Gaussian processes to efficiently model and compute counterparty credit valuation adjustments (CVA).
problem Efficiently modeling and computing CVA for large OTC derivative portfolios.
method Multi-Gaussian process regression approach to learn a metamodel for the mark-to-market cube of a derivative portfolio.
result The method accurately and efficiently computes CVA for interest rate swap portfolios.
Paper characterizes sampling distributions of optimal portfolio weights and characteristics.
problem Characterizing sampling distributions of optimal portfolio weights and characteristics.
method Derives exact sampling distribution by stochastic representation.
result High-dimensional asymptotic distribution of optimal portfolio weights is multivariate normal.
Optimizes portfolios with constraints and stochastic factors, deriving explicit solutions.
problem Optimizing expected utility in an incomplete market with stochastic factors and convex constraints.
method Fundamental duality results and HJB PDE, derived condition for exponential affine solutions.
result Explicit expressions for optimal allocations and Riccati ODE solutions in specific markets.
The paper explores arbitrage opportunities in derivative markets under specific conditions.
problem Arbitrage opportunities in derivative markets under different conditions.
method Analyzes the relationship between pricing kernel monotonicity and stochastic arbitrage opportunities.
result Pricing kernel nonmonotonicity is equivalent to stochastic arbitrage opportunities under adequacy.
We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we show that, under the usual no-arbitrage condition, the existence of a replicati…
Speeds up complex portfolio exposure calculations.
problem Calculating exposure of portfolios with exotic derivatives.
method Least Squares Monte Carlo (LSMC) technique.
result Significantly reduces computation time for nested Monte Carlo.
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with drift and volatility b…
We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not di…
Deep Bellman Hedging uses reinforcement learning to optimize financial portfolio hedging.
problem Optimizing financial portfolio hedging with derivatives and trading frictions.
method Actor-critic reinforcement learning algorithm with continuous state and action spaces.
result Trained model provides optimal hedge for any initial portfolio and market state.
The paper redefines semi-static hedging as derivatives and calculates hedging errors.
problem The costs of maintaining hedging portfolios and the limitations of semi-static hedging.
method New integral representations, approximations, and efficient numerical methods for calculating Wiener-Hopf factors and Laplace-Fourier inversion.
result The hedging error of static hedging portfolios can be larger than variance-minimizing portfolios.
We discuss the use of saddlepoint methods in the analysis of portfolios, with particular reference to credit portfolios. The objective is to proceed from a model of the loss distribution, given through probabilities, correlations and the like, to an analytical approximation of the distribution. Once this is done we sho…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved so…
Combines option pricing and portfolio theory for optimal hedging.
problem Optimal hedging of European options in various price dynamics.
method Derives optimal holdings and unhedged risk for different price dynamics.
result Derives solutions for various price dynamics including binomial, diffusion, volatility, volatility-of-volatility, and jump diffusion.
Markowitz simplified portfolio returns assuming constant trade volumes.
problem Understanding portfolio returns and variance in markets with variable trade volumes.
method Investor observes market trades, models portfolio as single security, derives portfolio return and variance.
result Markowitz's equation for portfolio returns and variance is a simplified approximation of real markets with constant trade volumes.
Develops SPT with price impact, deriving formulas for wealth and arbitrage conditions.
problem Tackles price impact in high-dimensional markets.
method Incorporates nonlinear price impact and impact decay models.
result Derives master formula for trading strategies and wealth dynamics.
We derive simple return models for several classes of bond portfolios. With only one or two risk factors our models are able to explain most of the return variations in portfolios of fixed rate government bonds, inflation linked government bonds and investment grade corporate bonds. The underlying risk factors have nat…
This paper develops a new portfolio optimization framework that considers network spillovers.
problem Modern financial markets' complex interconnections are not fully captured by variance alone.
method Formulates a three-objective optimization problem with a quadratic measure of network spillovers.
result Establishes a three-dimensional efficient surface and a risk-risk frontier.
Optimal portfolio yields a digital option payoff.
problem Portfolio optimization under generalized dual theory of choice.
method Characterized optimal solution and derived it in closed form.
result Payoff is a digital option that yields in-the-money payoff in good market scenarios.
We consider the problem of finding the efficient frontier associated with the risk-return portfolio optimization model. We derive the analytical expression of the efficient frontier for a portfolio of N risky assets, and for the case when a risk-free asset is added to the model. Also, we provide an R implementation, an…
A semi-static approach efficiently replicates and prices callable interest rate derivatives.
problem Efficiently replicating and pricing callable interest rate derivatives under dynamic market conditions.
method Proposes a semi-static hedging algorithm that updates the replication portfolio on a finite number of instances, rather than continuously.
result The hedging error can be made arbitrarily small with a sufficiently large replication portfolio, and closed-form error margins are determined.
The paper optimizes regret using covariance between costs and decisions.
problem Optimizing expected regret in decision-making problems.
method Developed derivative theory of covariance regret functional, derived Gâteaux derivative, and extended to constrained optimization.
result Gradient of covariance regret is the cost covariance matrix, with implications for portfolio optimization.
We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the evolution of dependent stochastic variables. We demonstrate this pr…
Machine learning factors outperform traditional portfolio optimization methods.
problem Comparing machine learning and traditional portfolio optimization methods.
method Examined machine learning and factor-based portfolio optimization using autoencoder neural networks and dimensionality reduction techniques.
result Minimum-variance portfolios using latent factors derived from autoencoders and sparse methods outperform simpler benchmarks in risk minimization.
Paper tackles P vs NP problem in portfolio optimization with cardinality constraints and Black-Scholes derivatives.
problem Operationalizing the P vs NP problem in cardinality-constrained portfolio selection.
method Mixed-integer quadratic program with genetic algorithms, Monte Carlo sampling, and greedy screening.
result Cardinality constraint reshapes efficient frontier, highlighting trade-offs between stability and computational cost.
Paper optimizes trend-following portfolios using autocorrelation models.
problem Developing an optimal trend-following portfolio strategy.
method Introduces a unifying theoretical setting with autocorrelation models for covariance matrices of trends and risk premia. Specifies practical models for covariance matrices. Decomposes optimal portfolio into four basic components.
result Empirical backtests confirm overperformance of the proposed optimal portfolio.
We use machine learning for designing a medium frequency trading strategy for a portfolio of 5 year and 10 year US Treasury note futures. We formulate this as a classification problem where we predict the weekly direction of movement of the portfolio using features extracted from a deep belief network trained on techni…
Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
Energy markets are strategic to governments and economic development. Several commodities compete as substitutable energy sources and energy diversifiers. Such competition reduces the energy vulnerability of countries as well as portfolios' risk exposure. Vulnerability results mainly from price trends and fluctuations,…
A deep Q-learning strategy optimizes portfolio trading efficiency.
problem Optimizing dynamic portfolio allocation schemes.
method Formulated a Markov decision process model with deep Q-learning for discrete combinatorial actions.
result Outperforms benchmark strategies in real-world trading simulations.
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal…
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect…
This paper calculates worst-case target semi-variances for uncertain losses.
problem Managing risk when loss distribution is uncertain and only partial information is known.
method Derives worst-case target semi-variances for symmetric or non-negative losses under uncertainty sets representing investor's undesirable scenarios.
result Closed-form expressions for worst-case target semi-variances are derived.
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide downside protection. A tractable stochastic mortality model with age dependent …
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is t…
Paper develops risk statistics for portfolios considering regulator-based risk.
problem Traditional risk statistics fail to describe regulator-based risk.
method Develop dual representation for regulator-based risk statistics.
result Derived dual representation for regulator-based risk statistics.
This paper proposes a new simulation-based VaR estimation method for complex portfolios.
problem Estimating VaR for portfolios with nonlinear derivatives is challenging.
method Develops a generic simulation-based algorithm that incorporates cross-sectional and variable selection techniques.
result The new approach converges faster and is more effective than existing methods.
New shrinkage estimator for GMV portfolio reduces risk in high-dimensional asset settings.
problem Estimating the global minimum variance portfolio in high-dimensional settings with limited data.
method Dynamic shrinkage of the GMV portfolio using previous data as a target.
result The new estimator outperforms traditional methods in high-dimensional asset settings.
Bayesian approach improves portfolio optimization using VaR and CVaR.
problem Optimizing portfolio weights using VaR and CVaR for risk management.
method Bayesian perspective, posterior predictive distribution, observed data.
result Bayesian approach yields more accurate optimal portfolio weights.
The paper optimizes portfolios using relative tail risk measures.
problem Optimizing portfolios with respect to relative tail risk.
method Analytic forms of portfolio CoVaR and CoCVaR derived on a market model. Monte-Carlo simulation for CoCVaR and marginal contributions. Risk budgeting method applied.
result Derivation of analytic forms for CoVaR and CoCVaR, and their marginal contributions.
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution of the underlying asset returns is fully known. In practice, both the performance…
Ensemble method for fast portfolio valuation and risk management.
problem Dynamic portfolio valuation and risk management from cash flow data.
method Regression trees for dynamic value process learning.
result Fast and accurate estimator with closed-form solution.
In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed a…