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Maximizing Utility of Consumption Subject to a Constraint on the Probability of Lifetime Ruin
Maximizing Utility Consumption Subject a Constraint Lifetime Ruin
2012/9/14
In this note, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which ...
A note on asymptotic exponential arbitrage with exponentially decaying failure probability
Asymptotic exponential arbitrage large deviations continuous semimartingale model.
2012/9/14
The goal of this paper is to prove a result conjectured in F¨ollmer and Schachermayer [FS07], even in slightly more general form. Suppose that Sis a continuous semimartingale and satisfies a large dev...
Bayesian logistic betting strategy against probability forecasting
exponential family game-theoretic probability Japan Meteorological Agency probability of precipitation strong law of large numbers
2012/4/28
We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove som...
Optimal Stopping under Probability Distortion
optimal stopping probability distortion Choquet expectation probability distribution/qunatile function Skorokhod embedding problem S-shaped and reverse S-shaped function
2011/3/31
We formulate an optimal stopping problem where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. ...
Transition Probability Matrix Methodology for Incremental Risk Charge
constructing transition TPMs the available historical data the merger of one-year Basel PD deriving a monthly
2011/3/23
As part of Basel II's incremental risk charge (IRC) methodology, this paper summarizes our extensive investigations of constructing transition probability matrices (TPMs) for unsecuritized credit prod...
Optimal control of a big financial company with debt liability under bankrupt probability constraints
Regular-singular stochastic optimal control Stochastic differential
2010/10/21
This paper considers an optimal control of a big financial company with debt liability under bankrupt probability constraints. The company, which faces constant liability payments and has choices to ...
Outperforming the Market Portfolio with a Given Probability
Market Portfolio Given Probability
2010/10/20
Our goal is to resolve a problem proposed by Karatzas and Fernholz (2008): Characterizing the minimum amount of initial capital that would guarantee the investor to beat the market portfolio with a c...
Statistical mechanics approach to the probability distribution of money
Statistical mechanics probability distribution of money
2010/10/21
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as r...
Bounds on Stock Price probability distributions in Local-Stochastic Volatility models
Law of the spot price local-stochastic volatility moment explosion
2010/10/20
We show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as...
Minimizing the Probability of Lifetime Ruin under Stochastic Volatility
Optimal investment minimizing the probability of lifetime ruin
2010/10/19
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 ma...
Ruin probability with Parisian delay for a spectrally negative Lévy risk process
Levy process ruin probability asymptotics Parisian ruin risk process
2010/4/27
In this paper we analyze so-called Parisian ruin probability that happens when surplus process stays below zero longer than fixed amount of time $\zeta>0$. We focus on general spectrally negative L\'{...
Asymptotics of the probability minimizing a "down-side" risk
probability minimizing down-side risk
2010/10/18
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation ...
The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map
alchemy probability distributions rank transmutation map
2010/10/29
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical app...
Optimal Reversible Annuities to Minimize the Probability of Lifetime Ruin
Optimal Reversible Annuities Minimize Probability Lifetime Ruin
2010/10/18
We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a l...
Does Security Transaction Volume-Price Behavior Resemble a Probability Wave?
Security Transaction Volume-Price Behavior Wave
2010/10/18
Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We ...