Related papers: Non-linear filtering and optimal investment under …
We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
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…
In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider…
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
This paper develops a continuous-time filtering framework for estimating a hazard rate subject to an unobservable change-point. This framework naturally arises in both financial and insurance applications, where the default intensity of a…
Dynamical systems with binary-valued observations are widely used in information industry, technology of biological pharmacy and other fields. Though there have been much efforts devoted to the identification of such systems, most of the…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility…
We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of…
Motivated by practical applications, we explore the constrained multi-period mean-variance portfolio selection problem within a market characterized by a dynamic factor model. This model captures predictability in asset returns driven by…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…
We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…
The classical state-space approach to optimal estimation of stochastic processes is efficient when the driving noises are generated by martingales. In particular, the weight function of the optimal linear filter, which solves a complicated…
We consider a stochastic financial incomplete market where the price processes are described by a vector-valued semimartingale that is possibly nonlocally bounded. We face the classical problem of utility maximization from terminal wealth,…
No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset…
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular,…
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price…