Stochastic Factor Model Research Articles

Power Forward Performance in Semimartingale Markets with Stochastic Integrated Factors

We study the forward investment performance process (FIPP) in an incomplete semimartingale market model with closed and convex portfolio constraints, when the investor’s risk preferences are of the power form. We provide necessary and sufficient conditions for the existence of such a FIPP. In a semimartingale factor model, we show that the FIPP can be recovered as a triplet of processes that admit an integral representation with respect to semimartingales. Using an integrated stochastic factor model, we relate the factor representation of the triplet of processes to the smooth solution of an ill-posed partial integro-differential Hamilton–Jacobi–Bellman equation. We develop explicit constructions for the class of time-monotone FIPPs, generalizing existing results from Brownian to semimartingale market models. Funding: L. Bo was supported by the National Natural Science Foundation of China (NSFC) [Grant 11971368] and National Center for Applied Mathematics in Shaanxi (NCAMS). A. Capponi was supported in part by the National Science Foundation [Grant DMS-1716145]. C. Zhou was supported by the Singapore Ministry of Education Academic Research Fund [Grant R-146-000-271-112] and NSFC [Grant 11871364].

Optimal investment and reinsurance of insurers with lognormal stochastic factor model

<p style='text-indent:20px;'>We propose the stochastic factor model of optimal investment and reinsurance of insurers where the wealth processes are described by a bank account and a risk asset for investment and a Cramér-Lundberg process for reinsurance. The optimization is obtained through maximizing the exponential utility. Owing to the claims driven by a Poisson process, the proposed optimization problem is naturally treated as a jump-diffusion control problem. Applying the dynamic programming, we have the Hamilton-Jacobi-Bellman (HJB) equations and the corresponding explicit solution for the corresponding HJB. Hence, the optimal values and optimal strategies can be obtained. Finally, in numerical analysis, we illustrate the performance of the proposed optimization according to the results of the corresponding value function. In addition, compared to the wealth process without investment, the efficiency of the proposed optimization is discussed in terms of ruin probabilities.</p>

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty ...

What Uncertainties Matter to Cryptocurrencies?

We contribute to financial literature by identifying economic uncertainties salient to the price dynamics of cryptocurrencies. To measure this relationship, we examine the common stochastic trends between cryptocurrencies and major text-based uncertainty indices — categorical and broad — from the US and major developed economies from 2015 to 2021. Results from static factor tests using high-dimensional stochastic volatility factor models indicate trivial associations between global uncertainties and the crypto-sphere. Further investigation from dynamic implied correlation matrices, however, suggest that this phenomenon has undergone several changes over time. In fact, ties between US-based monetary policy uncertainties were non-trivial between 2015 to 2016. Following the post-Trump election bull run, the association faded, before reappearing upon the advent of the COVID-19 pandemic. Uncertainties surrounding some decisions by US government register minor significance. Uncertainties from European countries and China show some influence, with Japan registering an inverse relationship. Causality tests largely approbate these results, while underscoring an important point that while the pricing dynamics of cryptocurrencies may be independent from global uncertainties, their second moments remain attached to global trends. In sum, volatility in the crypto market is impacted by global uncertainties; prices are less so.

ТЕОРЕТИКО-МЕТОДИЧНІ ЗАСАДИ ІДЕНТИФІКАЦІЇ ВНУТРІШНІХ ФАКТОРІВ ФУНДАМЕНТАЛЬНО-СТЕЙКХОЛДЕРСЬКОЇ ДОДАНОЇ ВАРТОСТІ ПІДПРИЄМСТВ

In the article it is researched the development of theoretical and methodological grounds of identification of internal factors of the fundamental and stakeholder value added of enterprises in the process of implementing the system of value-based management at the microeconomic level on the basis of the factor approach. The fundamental and stakeholder value added of enterprises is considered as the factor system, the elements of which are its internal factors. The problem of substantiation of the type of a factor model for studying the dependence of the fundamental and stakeholder value added of enterprises on its internal factors has been researched. A structural and logical model for calculating the fundamental and stakeholder value added of enterprises as a multifactorial phenomenon has been developed. The indicators that are directly involved in calculation of the fundamental and stakeholder value added of enterprises have been studied. It is revealed the connection with the scope of internal and external factors of those indicators which are directly involved in the calculation of the fundamental and stakeholder value added of enterprises. There was substantiated the necessity of building a stochastic factor model for the formalized determination of the mathematical dependence of the fundamental and stakeholder value added of enterprises on its internal factors. It is determined the expediency of applying the correlation and regression method in the process of stochastic modeling of the factor system, in which internal factors and the fundamental and stakeholder value added of enterprises are united by one cause- and-effect relationship. There has been studied the problem of identification of those internal factors which have the most probable influence on the fundamental and stakeholder value added of enterprises in econometric modeling using the correlation and regression method. It is revealed the content of transformation of factor indicators while building a multiple regression model to study the dependence of the fundamental and stakeholder value added of enterprises on its internal factors. In the process of correlation and regression modeling the internal factors of the fundamental and stakeholder value added and their indicators are determined.

Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a large class of forward performance processes, as well as the corresponding optimal portfolios, with power-utility initial data and for stock–factor correlation matrices with eigenvalue equality (EVE) structure, which we introduce here. This is done by solving the associated nonlinear parabolic partial differential equations (PDEs) posed in the “wrong” time direction. Along the way, we establish on domains an explicit form of the generalised Widder theorem of Nadtochiy and Tehranchi (Math. Finance 27:438–470, 2015, Theorem 3.12) and rely for that on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the “right” time direction.

A note on monotone mean–variance preferences for continuous processes

We extend a recent result of Trybuła and Zawisza (2019), who investigate a continuous-time portfolio optimization problem under monotone mean–variance preferences. Their main finding is that the optimal strategies for monotone and classical mean–variance preferences coincide in a stochastic factor model for the financial market. We generalize this result to any model for the financial market where asset prices are continuous.

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the dynamics of the underlying stocks depends on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the power robust forward performance process in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical power robust expected utility for long time horizons.

Optimal investment-consumption-insurance with partial information

We consider an optimal investment, consumption, and life insurance purchase problem for a wage earner. We treat a stochastic factor model that the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case that the wage earner can not observe the factor process and use only past information of risky assets. Then, our problem is formulated as a stochastic control problem with partial information. Applying the dynamic programming principle, we derive a coupled system of the Hamilton–Jacobi–Bellman (HJB) equation and two backward stochastic differential equations (BSDEs), and obtain the explicit solution. Finally, we strictly prove the verification theorem, and construct the optimal investment-consumption-insurance strategy.

Joint Modeling of Longitudinal Relational Data and Exogenous Variables

This article proposes a framework based on shared, time varying stochastic latent factor models for modeling relational data in which network and node-attributes co-evolve over time. Our proposed framework is flexible enough to handle both categorical and continuous attributes, allows us to estimate the dimension of the latent social space, and automatically yields Bayesian hypothesis tests for the association between network structure and nodal attributes. Additionally, the model is easy to compute and readily yields inference and prediction for missing link between nodes. We employ our model framework to study co-evolution of international relations between 22 countries and the country specific indicators over a period of 11 years.

Optimal proportional reinsurance and investment for stochastic factor models

In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend the classical Cramér–Lundberg model introducing a stochastic factor which affects the intensity of the claims arrival process, described by a Cox process, as well as the insurance and reinsurance premia. The financial market is supposed not influenced by the stochastic factor, hence it is independent on the insurance market. Using the classical stochastic control approach based on the Hamilton–Jacobi–Bellman equation we characterize the optimal strategy and provide a verification result for the value function via classical solutions to two backward partial differential equations. Existence and uniqueness of these solutions are discussed. Results under various premium calculation principles are illustrated and a new premium calculation rule is proposed in order to get more realistic strategies and to better fit our stochastic factor model. Finally, numerical simulations are performed to obtain sensitivity analyses.

A Note on Monotone Mean-Variance Preferences for Continuous Processes

We extend a recent result of Trybula and Zawisza [Mathematics of Operations Research, 44(3), 966-987, 2019], who investigate a continuous-time portfolio optimization problem under monotone mean-variance preferences. Their main finding is that the optimal strategies for monotone and classical mean-variance preferences coincide in a stochastic factor model for the financial market. We generalize this result to any model for the financial market where stock prices are continuous.

An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior

Using elements from the theory of ergodic backward stochastic differential equations (BSDEs), we study the behavior of forward entropic risk measures in stochastic factor models. We derive general representation results (via both BSDEs and convex duality) and examine their asymptotic behavior for risk positions of large maturities. We also compare them with their classical counterparts and provide a parity result.

An optimal consumption and investment problem with partial information

AbstractWe consider a finite-time optimal consumption problem where an investor wants to maximize the expected hyperbolic absolute risk aversion utility of consumption and terminal wealth. We treat a stochastic factor model in which the mean returns of risky assets depend linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. We discuss the partial information case in which the investor cannot observe the factor process and uses only past information of risky assets. Then our problem is formulated as a stochastic control problem with partial information. We derive the Hamilton–Jacobi–Bellman equation. We solve this equation to obtain an explicit form of the value function and the optimal strategy for this problem. Moreover, we also introduce the results obtained by the martingale method.

A maximum principle for controlled stochastic factor model

In the present work, we consider an optimal control for a three-factor stochastic factor model. We assume that one of the factors is not observed and use classical filtering technique to transform the partial observation control problem for stochastic differential equation (SDE) to a full observation control problem for stochastic partial differential equation (SPDE). We then give a sufficient maximum principle for a system of controlled SDEs and degenerate SPDE. We also derive an equivalent stochastic maximum principle. We apply the obtained results to study a pricing and hedging problem of a commodity derivative at a given location, when the convenience yield is not observable.

Portfolio management in a stochastic factor model under the existence of private information

Portfolio management in a stochastic factor model under the existence of private information

Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty

We theoretically and empirically study large-scale portfolio allocation problems when transaction costs are taken into account in the optimization problem. We show that transaction costs act on the one hand as a turnover penalization and on the other hand as a regularization, which shrinks the covariance matrix. As an empirical framework, we propose a flexible econometric setting for portfolio optimization under transaction costs, which incorporates parameter uncertainty and combines predictive distributions of individual models using optimal prediction pooling. We consider predictive distributions resulting from highfrequency based covariance matrix estimates, daily stochastic volatility factor models and regularized rolling window covariance estimates, among others. Using data capturing several hundred Nasdaq stocks over more than 10 years, we illustrate that transaction cost regularization (even to small extent) is crucial in order to produce allocations with positive Sharpe ratios. We moreover show that performance differences between individual models decline when transaction costs are considered. Nevertheless, it turns out that adaptive mixtures based on high-frequency and low-frequency information yield the highest performance. Portfolio bootstrap reveals that naive 1=N-allocations and global minimum variance allocations (with and without short sales constraints) are significantly outperformed in terms of Sharpe ratios and utility gains.

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.

A stochastic volatility factor model of heston type. Statistical properties and estimation

In this paper we study the properties of a new multidimensional continuous-time stochastic covariance process, the Stochastic Volatility Factor model. Two helpful conditional characteristic functions, one needed for estimation and the other used in the pricing of financial derivatives are provided, together with the properties of the instantaneous dependence structure. Conditions for stationarity, ergodicity and mixing properties of the increments are studied. The estimation of the model is performed using the Continuum-Generalized Method of Moments (CGMM). A simulation exercise is included showing parameters are recovered, confirming identifiability. The model is also calibrated to exemplary financial data.

Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov–Galerkin method

The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options, mesh-based methods are applied in a number of papers but it is well-known that these methods depend strongly on the mesh properties which is the major disadvantage of them. Therefore, we propose the use of the meshless methods to solve the aforementioned options models, especially in this work we select and analyze one scheme of them, named local radial point interpolation (LRPI) based on Wendland's compactly supported radial basis functions (WCS-RBFs) with C6 , C4 and C2 smoothness degrees. The LRPI method which is a special type of meshless local Petrov–Galerkin method (MLPG), offers several advantages over the mesh-based methods, nevertheless it has never been applied to option pricing, at least to the very best of our knowledge. These schemes are the truly meshless methods, because, a traditional non-overlapping continuous mesh is not required, neither for the construction of the shape functions, nor for the integration of the local sub-domains. In this work, the American option which is a free boundary problem, is reduced to a problem with fixed boundary using a Richardson extrapolation technique. Then the implicit–explicit (IMEX) time stepping scheme is employed for the time derivative. Numerical experiments are presented showing that the proposed approaches are extremely accurate and fast.