Optimizes reinsurance and investment strategies to minimize ruin probability.
problem Optimizing reinsurance and investment strategies to minimize ruin probability.
method Stochastic projected gradient method based on Malliavin calculus.
result Effectiveness of the proposed method demonstrated through numerical experiments.
The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
Investment and consumption strategy for risk-averse agents with Epstein-Zin utility.
problem Optimal investment and consumption strategy for Epstein-Zin utility.
method Detailed introduction to Epstein-Zin utility, existence and uniqueness proof, verification argument.
result Existence and uniqueness of optimal solution for Epstein-Zin utility under certain parameter restrictions.
Paper applies theorem to find optimal investment boundary in stochastic capacity expansion.
problem Finding optimal investment boundary in a stochastic, time-inhomogeneous capacity expansion problem.
method Applies Bank and El Karoui Representation Theorem to solve first order conditions involving a non-integral term.
result Existence of base capacity ly⋆(t), showing optimal investment process becomes active at this level. The Kelly rule fails to maximize growth in a time-changed return setting.
problem Performance of the Kelly rule in a time-changed return process.
method Investigated the Kelly rule in a semi-martingale setting with a time change process.
result The Kelly rule does not maximize average growth rate in a non-normal log-return setting.
Investor optimizes investment and consumption under uncertain market conditions with constraints.
problem Investor optimizes investment and consumption in a stochastic environment with model uncertainty and constraints.
method Robust control problem solved using stochastic Hamilton-Jacobi-Bellman-Isaacs equations, backward stochastic differential equations, and bounded mean oscillation martingale theory.
result Investor incurs utility loss when ignoring model uncertainty, and constraints impact optimal strategy and value function.
Study optimal investment and reinsurance strategy for insurers under random coefficients.
problem Optimal mean-variance investment-reinsurance problem for insurers under Cramér-Lundberg model with random coefficients.
method Reduced to a constrained stochastic linear-quadratic control problem with jumps, solved using BSDE techniques and SREs.
result Explicit efficient investment-reinsurance strategy and mean-variance frontier.
Model for optimal cybersecurity investment considering clustered cyberattacks.
problem Optimal investment in cybersecurity to reduce system vulnerability under clustered cyberattacks.
method Developed a continuous-time stochastic model using a Hawkes process, extended Gordon-Loeb model, solved as a Markovian stochastic optimal control problem.
result Investment policies that account for attack clustering lead to more effective and responsive strategies, improving upon static and Poisson-based approaches.
Investment strategies in occupational pension plans are optimized for non-tradable income risk.
problem Optimizing investment strategies for occupational pension plans in the presence of non-tradable income risk.
method Formulated as a stochastic optimization problem, analyzed in both constant and stochastic volatility environments.
result Random contributions induce the optimal glide path structure, influenced by initial wealth, contributions, and risk aversion.
Study optimal investment under uncertain conditions.
problem Optimal investment in uncertain market conditions.
method Modelled Knightian uncertainty through multiple priors, solved using stochastic backward equations.
result Existence and uniqueness of optimal investment plan derived.
Optimal insurance and investment strategy under exponential preferences in a correlated market model.
problem Optimal investment and reinsurance strategy for an insurance company under exponential preferences.
method Stochastic control techniques to construct a forward dynamic exponential utility and characterize the optimal strategy.
result Characterization of the optimal investment and reinsurance strategy in a correlated market model.
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using tools from stochastic control, and how to rigorously verify their optimality by mea…
The paper solves a consumption-investment problem with state-dependent lower bounds.
problem A life-time consumption-investment problem with a state-dependent lower bound on consumption.
method Transformed the problem into a state-independent control problem to apply standard theory.
result Explicit optimal strategies provided for both homogeneous and non-homogeneous constraints.
This research tackles backdoor attacks on audio data using a stochastic investment approach.
problem The threat of backdoor attacks on audio data, especially in voice-activated systems.
method A Stochastic investment-based backdoor attack (MarketBack) approach.
result MarketBack can achieve an average attack success rate close to 100% with less than 1% of poisoned data.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
Investor optimizes stock investments with noisy future price signals.
problem Optimizing stock investments with uncertain future stock prices.
method Dynamic investment strategy with partial observation of Brownian motion.
result Closed-form solution for optimal investment problem.
In this paper we propose a novel application of Gaussian processes (GPs) to financial asset allocation. Our approach is deeply rooted in Stochastic Portfolio Theory (SPT), a stochastic analysis framework introduced by Robert Fernholz that aims at flexibly analysing the performance of certain investment strategies in st…
Study optimal investment and consumption in a stochastic factor model.
problem Optimal investment and consumption decisions in a stochastic factor model.
method Characterization of well-posedness, numerical algorithm, and general theory of sub- and supersolutions for HJB equation.
result Proves existence and provides bounds for the solution to the HJB equation.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
Study BSΔE on lattices for asset price analysis.
problem Optimal investment and market equilibrium analysis in asset price models.
method Backward stochastic difference equations on lattices.
result Applications to optimal investment and market equilibrium analysis.
We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter's price following a diffusion with stochastic volatility. In the current financial market especially, it is important to include stochastic volatility in the risky asset's price process. Given the rate of c…
In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize…
The paper calculates how fast optimal investment strategies approach CRRA strategies in stochastic factor models.
problem Understanding convergence rates of optimal investment strategies in stochastic factor models.
method Analyzes optimal feedback functions in nonlinear and quadratic term structure models, considering decay of bond prices and power-like utility at high wealth levels.
result Convergence rates of optimal investment strategies to CRRA strategies are determined by bond price decay and power-like utility behavior.
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.
In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and life insurance problem with stochastic volatility, that is, we consider a wage earn…
This paper is devoted to study the effects arising from imposing a value-at-risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a continuous-time financial market. For simplicity, we assume that there is only one investm…
In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic volatility and a defaultable corporate bond. We discuss the optimal investment …
Paper solves a control problem with robust methods.
problem Monotone mean-variance problems with stochastic coefficients.
method Finding saddle point through BSDEs with unbounded coefficients.
result Optimal control and value match mean-variance problems.
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Revisits consumption-investment problem with anticipative noise.
problem Revisits classical consumption-investment problem with anticipative noise.
method Models risky-asset returns through a general α-integral, interpolating between Itô, Stratonovich, and related conventions.
result Derives closed-form optimal policies for logarithmic utility and constant volatilities in a market with n risky assets.
New method finds profitable investment opportunities by considering additional financial variables.
problem Finding trading strategies that outperform the market with high probability.
method Generalizing functionally generated portfolios to include continuous-path semimartingales.
result Inclusion of additional processes can reduce time horizons for profitable arbitrage opportunities.
This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium…
Study forward investment performance in semimartingale markets with stochastic factors.
problem Investigate forward investment performance in incomplete semimartingale markets with power risk preferences and stochastic integrated factors.
method Develop necessary and sufficient conditions for FIPP existence, use integral representations, and solve ill-posed HJB equations.
result Explicit constructions for time-monotone FIPPs in semimartingale models, generalizing from Brownian to semimartingale markets.
This paper revisits optimal investment strategies for defined contribution pension schemes using forward preferences.
problem Optimal investment strategies derived from backward models are not time-consistent and sub-optimal in real scenarios.
method Introduces forward preferences and solves optimal investment strategies for defined contribution pension schemes.
result Constructs optimal investment strategies for defined contribution pension schemes using forward preferences.
Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use the dynami…
Study optimal reinsurance and investment strategies under common shocks affecting financial and actuarial markets.
problem Maximizing expected exponential utility of terminal wealth in a company facing both ordinary and catastrophic claims.
method Modeling common shocks affecting financial and actuarial markets, using stochastic control and Hamilton-Jacobi-Bellman equations.
result Characterization of optimal reinsurance and investment strategies under common shock dependence.
We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial market is affected by the optimal liquidation of an independent indivisible asset…
New optimal investment strategies for finance and insurance using Hawkes-based models.
problem Optimal investment strategies in finance and insurance for specific models.
method Solving Merton investment problems with Hawkes-based models.
result New optimal investment results for finance and insurance models.
In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve according to quite general semimartingales. We show that the ruin problem corresponds to…
Enhances robo-advisors with client investment preference inference.
problem Accurately inferring clients' investment preferences from past activities.
method Stochastic control framework with continuous-time model and discounting scheme.
result Proves sufficient conditions for client investment preference identifiability.
Study time-inconsistent consumption-investment in incomplete markets with general discount functions.
problem Time-inconsistent consumption-investment problems in incomplete markets.
method Coupled forward-backward stochastic differential equation approach.
result Uniqueness of open-loop equilibrium pair proved.
Solves the Merton investment-consumption problem using a new approach.
problem Infinite-horizon Merton investment-consumption problem in a constant-parameter Black-Scholes-Merton market.
method Simple and elegant argument involving a stochastic perturbation of the utility function.
result Overcomes complications in existing primal verification proofs.
In life-cycle economics the Samuelson paradigm (Samuelson, 1969) states that the optimal investment is in constant proportions out of lifetime wealth composed of current savings and the present value of future income. It is well known that in the presence of credit constraints this paradigm no longer applies. Instead, …
Investment decision triggered by a convex curve in a two-factor uncertainty model.
problem Optimal irreversible investment in a company with two products whose prices follow geometric Brownian motions.
method Two-dimensional optimal stopping problem, nonlinear integral equation, convex curve characterization.
result Optimal investment decision is characterized by a convex curve, unique solution to a nonlinear integral equation.
We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment strategies) and ask if it is possible to derive a utility function for which the observ…
Assume (1) asset returns follow a stochastic multi-factor process with time-varying conditional expectations; (2) investments are linear functions of factors. This paper calculates asymptotic joint moments of the logarithm of investor's wealth and the factors. These formulas enable fast computation of a wide range of i…
Investigates optimal consumption and investment strategies with constraints in incomplete markets.
problem Optimal consumption and investment under constraints in incomplete markets.
method Characterizes optimal strategies via a quadratic BSDE, using martingale optimality criterion and Lyapunov functions.
result Obtains the verification theorem for optimal strategies in unbounded cases.