arXiv subjects

Mauricio Elizalde

Publications and source records attributed to Mauricio Elizalde.

4 recordsLinked to original sources

arXiv2024

Intertemporal Cost-efficient Consumption

We aim to provide an intertemporal, cost-efficient consumption model that extends the consumption optimization inspired by the Distribution Builder, a tool developed by Sharpe, Johnson, and Goldstein. The Distribution Builder enables the recovery of investors' risk preferences by allowing them to select a desired distribution of terminal wealth within their budget constraints. This approach differs from the classical portfolio optimization, which considers the agent's risk aversion modeled by utility functions that are challenging to measure in practice. Our intertemporal model captures the dependent structure between consumption periods using copulas. This strategy is demonstrated using both the Black-Scholes and CEV models.

q-fin.MF↗

arXiv2023

Properties and approximations of fractions associated to Ford circles extracted by inclined lines

We study fractions associated to Ford circles which are extracted by means continuous curves. We show that the extracted fractions have similar properties to Farey sequences, like the Farey sum, and we prove that every ordered sequence that satisfies the Farey sum and has two adjacent fractions, can be extracted from Ford circles through continuous curves. This allows us to relate sequences of fractions that satisfy the Farey sum and continuous curves. We focus on the fractions $F_{1/m}$ extracted from inclined lines with positive slopes of the form $1/m$ and define jumps as the cardinality increments of these fractions with respect to $m$. We relate the expression for every jump to the prime omega function in terms of $m$ and find a cardinality formula related to the Möbius function, which we approximate with three tractable expressions that grow in a log-linear way considering estimations of sums related to Euler's totient function or the graph of the lattice points corresponding to the fractions $p/q$.

math.NT↗

arXiv2022

Optimal investment with insider information using Skorokhod & Russo-Vallois integration

We study the maximization of the logarithmic utility for an insider with different anticipating techniques. Our aim is to compare the utilization of Russo-Vallois forward and Skorokhod integrals in this context. Theoretical analysis and illustrative numerical examples showcase that the Skorokhod insider outperforms the forward insider. This remarkable observation stands in contrast to the scenario involving risk-neutral traders. Furthermore, an ordinary trader could surpass both insiders if a significant negative fluctuation in the driving stochastic process leads to a sufficiently negative final value. These findings underline the intricate interplay between anticipating stochastic calculus and nonlinear utilities, which may yield non-intuitive results from the financial viewpoint.

math.OC↗

arXiv2022

Chances for the honest in honest versus insider trading

We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Doléans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.

math.PR↗