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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...
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...
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 ...
Scaling conditional tail probability and quantile estimators
distria relatively high frequency quantile estimates
2011/3/31
We present a novel procedure for scaling relatively high frequency tail probability and quantile estimates for the conditional distria.
We consider an insurance company in the case when the premium rate is a bounded non-negative random function $c_\zs{t}$ and the capital of the insurance company is invested in a risky asset whose pri...