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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
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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.
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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
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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
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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. ...
Representing filtration consistent nonlinear expectations as $g$-expectations in general probability spaces
nonlinear expectations comparison theorem nonlinear Doob-Meyer
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2011/3/23
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear...
Representing filtration consistent nonlinear expectations as $g$-expectations in general probability spaces
nonlinear expectations comparison theorem nonlinear Doob-Meyer
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2011/3/23
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear...
Parisian ruin probability for spectrally negative Lévy processes
L´ evy process ruin probability Parisian ruin risk process
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2011/3/23
In this note we give, for a spectrally negative L\'evy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below ze...
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
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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...
Optimization of dividend and reinsurance strategies under ruin probability constraint
Nonlinear regular-singular stochastic optimal control Ruin
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2010/10/20
This paper considers nonlinear regular-singular stochastic optimal control of large insurance company. The company controls the reinsurance rate and dividend payout process to maximize the expected p...
Optimal control of a big financial company with debt liability under bankrupt probability constraints
Regular-singular stochastic optimal control Stochastic differential
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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 ...
Continuous-time trading and the emergence of probability
Continuous-time trading emergence of probability
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2010/11/1
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized ...
Outperforming the Market Portfolio with a Given Probability
Market Portfolio Given Probability
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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
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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
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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
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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...