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We propose a machine learning-based methodology which makes use of ensemble methods with the aims (i) of treating missing data in time series with irregular observation times and detecting anomalies in the observed time behavior; (ii) of defining suitable models of the system dynamics. We applied this methodology to US wholesale electricity price time series that are characterized by missing data, high and stochastic volatility, jumps and pronounced spikes. For missing data, we provide a repair approach based on the missForest algorithm, an imputation algorithm which is completely agnostic about the data distribution. To identify anomalies, i.e., turbulent movements of power prices in which jumps and spikes are observed, we took into account the no-gap reconstructed electricity price time series, and then we detected anomalous regions using the isolation forest algorithm, an anomaly detection method that isolates anomalies instead of profiling normal data points as in the most common techniques. After removing anomalies, the additional gaps will be newly filled by the missForest imputation algorithm. In this way, a complete and clean time series describing the stable dynamics of power prices can be obtained. The decoupling between the stable motion and the turbulent motion allows us to define suitable jump-diffusion models of power prices and to provide an estimation procedure that uses the full information contained in both the stable and the turbulent dynamics.

A barrier option is an exotic path-dependent option contract where the right to buy or sell is activated or extinguished when the underlying asset reaches a certain barrier price during the lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing formulas for barrier options with general payoffs and exponential barriers on underlying assets that have jump-diffusion dynamics. With the same approach we also price barrier options on underlying futures contracts.

Stock return prediction for quantitative trading in U.S. equity markets has evolved from parametric econometric modeling toward data-driven deep learning systems that must jointly capture temporal dynamics, discontinuous jumps, and evolving cross-asset dependencies. Existing approaches still face three key challenges in deep learning-based stock return prediction: jump-aware temporal modeling is often missing or handled by ad hoc heuristics; higher-order stock relations are frequently encoded by static graphs/hypergraphs that do not adapt across market conditions, and temporal and relational learning are commonly implemented as sequential blocks with limited bidirectional interaction. We propose LévyHyper, an end-to-end framework that unifies jump-aware temporal encoding with regime-adaptive dynamic hypergraph learning and multi-scale hypergraph reasoning. LévyHyper integrates a neural jump-aware temporal layer motivated by Lévy jump-diffusion modeling, a regime-weighted fusion of predefined and learned hyperedges via a differentiable constructor, and a multi-scale hypergraph convolution module for hierarchical temporal aggregation. Experiments on S&P 500 data (463 stocks, 10 evaluation phases, prediction horizon τ=5 trading days) show that LévyHyper improves IC/RankIC and portfolio-level Sharpe ratio over strong baselines on average. We additionally report uncertainty estimates, significance tests, and transaction-cost sensitivity to support robust conclusions.

This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed.

In response to global aging challenges, establishing a sustainable pension investment management system has become crucial. This study proposes a defined-contribution (DC) pension risk mitigation framework that integrates investment and reinsurance strategies. Within this framework, we construct an investment game model of non-zero-sum for two pension investors with wealth maximization goals, allowing allocations to risk-free assets, risky assets, and reinsurance contracts. The higher-risk assets' time-varying market risk is modeled using the Heston Model which is characterized by stochastic volatility with mean-reversion. And the reinsurance surplus is denoted by a jump-diffusion model to capture the sudden financial shocks. Moreover, by utilizing standard dynamic programming and exponential utility preferences, we can derive a closed solution to the investment strategy throughout mathematical proofs. Our new model innovatively combines jump-diffusion processes with stochastic volatility from the Heston Model, expanding the theoretical foundation for pension investment optimization strategies. Practically, it offers pension managers a dynamic asset allocation tool which can increase portfolios' resistance to systemic risks.

We propose a stochastic model of infectious disease transmission that is more realistic than those found in the literature. The model is based on jump-diffusion processes. However, it is defined in such a way that the number of people susceptible to be infected decreases over time, which is the case for a population of fixed size. Next, we consider the problem of finding the optimal control of the proposed model. The dynamic programming equation satisfied by the value function is derived. Estimators of the various model parameters are obtained.

We work on a portfolio management problem for one agent and a large group of agents under relative performance concerns in jump-diffusion markets with the CRRA utility function. Herein, we define two wealth dynamics: the agent’s and the group’s wealth. We measure the performances of both the agent and the group with preferences linked to the group performance. Therefore, we have stochastic optimal control problems for both the representative agent and the group to determine what the group does and the agent’s optimal proportion in the portfolio relative to the group’s performance. Further, our framework assumes that the agent’s performance does not affect the group, while the group affects the agent’s utility. Moreover, we investigate special cases where all agents in the market are homogeneous in their risk aversion and relative performances. We explore the qualitative behavior of the agent and show some numerical results depending on her relative performance consideration and risk tolerance degree.

This paper investigates the optimal investment decision for an investor with partial information under the criterion of maximizing the expected utility of terminal wealth. The domestic and foreign stock prices, as well as the exchange rate, are modeled as jump-diffusion processes with stochastic coefficients. By employing Malliavin calculus, we derive a sufficient and necessary condition for the optimal investment strategy in cross-border transactions. In some special cases, a closed-form expression is obtained. Finally, a numerical example is provided to illustrate the impacts of parameters ρ1 , ρ2 , and σR on the optimal investment strategy.

This study investigates an optimal consumption–investment problem in which the unobserved stock trend is modulated by a hidden Markov chain that represents different economic regimes. In the classic approach, the hidden state is estimated using historical asset prices, but recent technological advances now enable investors to consider alternative data in their decision-making. These data, such as social media commentary, expert opinions, COVID-19 pandemic data and GPS data, come from sources other than standard market data sources but are useful for predicting stock trends. We develop a novel duality theory for this problem and consider a jump-diffusion process for alternative data series. This theory helps investors identify “useful” alternative data for dynamic decision-making by providing conditions for the filter equation that enable the use of a control approach based on the dynamic programming principle. We apply our theory to provide a unique smooth solution for an agent with constant relative risk aversion once the distributions of the signals generated from alternative data satisfy a bounded likelihood ratio condition. In doing so, we obtain an explicit consumption–investment strategy that takes advantage of different types of alternative data that have not been addressed in the literature.

Here we study the problems of probabilistic and quantile optimization of multidimensional controllable jump diffusion. As the main tool we use Chebyshev-type probability estimates. With them the problems under consideration are reduced to one auxiliary deterministic optimal control problem in terms of the moment characteristics of the process. To find its solution, we use Krotov’s global improvement method.