Related papers: Stochastic factors can matter: improving robust gr…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
Although financial models violate ergodicity in general, observing the ergodic behavior in the markets is not rare. Policymakers and market participants control the market behavior in critical and emergency states, which leads to some…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
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.…
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often such flexible policies are not desirable, and the…
Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
We introduce data-driven decision-making algorithms that achieve state-of-the-art \emph{dynamic regret} bounds for non-stationary bandit settings. These settings capture applications such as advertisement allocation, dynamic pricing, and…
We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
Signals coming from multivariate higher order conditional moments as well as the information contained in exogenous covariates, can be effectively exploited by rational investors to allocate their wealth among different risky investment…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
We revisit optimal execution of an active portfolio in the presence of slippage (aka linear, proportional, or absolute-value) costs. Market efficiency implies a close balance between active alphas and trading costs, so even small changes to…
Ergodicity economics is a new branch of economic theory that notes the conceptual difference between time averages and expectation values, which coincide only for ergodic observables. It postulates that individual agents maximise the time…
This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To…