Related papers: Polynomial processes in stochastic portfolio theor…
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…
We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the…
As the number of publicly traded companies as well as the amount of their financial data grows rapidly, it is highly desired to have tracking, analysis, and eventually stock selections automated. There have been few works focusing on…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this…
This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded $d$-dimensional semimartingale, we elaborate a complete and explicit characterization for…
This paper is concerned with portfolio selection for an investor with power utility in multi-asset financial markets in a rough stochastic environment. We investigate Merton's portfolio problem for different multivariate Volterra models,…
In recent years, the economic policy of privatization, which is defined as the transfer of property or responsibility from public sector to private sector, is one of the global phenomenon that increases use of markets to allocate resources.…
In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
This paper considers the finite horizon portfolio rebalancing problem in terms of mean-variance optimization, where decisions are made based on current information on asset returns and transaction costs. The study's novelty is that the…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
We study the class of continuous polynomial Volterra processes, which we define as solutions to stochastic Volterra equations driven by a continuous semimartingale with affine drift and quadratic diffusion matrix in the state of the…
Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…
We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Convergence rate for the total variation metric is derived using Lyapunov functions. Sharp fluctuations of…