Related papers: Dynamic asset trees and portfolio analysis
We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns, we derive approximate analytical results for the optimal investment fractions in various settings.…
Consider~\(n\) nodes distributed independently across~\(N\) cities contained with the unit square~\(S\) according to a distribution~\(f.\) Each city is modelled as an~\(r_n \times r_n\) square contained within~\(S\) and~\(MSTC_n\) denotes…
Despite the knowledge that social, economical, and ecological networks are often of a small-world nature with inter-nodal distance growing even slower than logarithmically with system size, we often assume theoretical systems to be outside…
We consider a model of directed polymers on a regular tree with a disorder given by independent, identically distributed weights attached to the vertices. For suitable weight distributions this model undergoes a phase transition with…
We consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal…
This paper investigates dynamic and static fund separations and their stability for long-term optimal investments under three model classes. An investor maximizes the expected utility with constant relative risk aversion under an incomplete…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
In this study, we propose a new multi-objective portfolio optimization with idiosyncratic and systemic risks for financial networks. The two risks are measured by the idiosyncratic variance and the network clustering coefficient derived…
We introduce a Markov Chain Monte Carlo algorithm which samples from the space of spanning trees of complete graphs using local rewiring operations only. The probability distribution of graphs of this kind is shown to depend on the…
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the…
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal…
Financial market is an example of complex system, which is characterized by a highly intricate organization and the emergence of collective behavior. In this paper, we quantify this emergent dynamics in the financial market by using…
Markowitz's criterion aims to balance expected return and risk when optimizing the portfolio. The expected return level is usually fixed according to the risk appetite of an investor, then the risk is minimized at this fixed return level.…
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is…