Jose M Corcuera - Academia.edu (original) (raw)

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Papers by Jose M Corcuera

Research paper thumbnail of Approximate predictive pivots for autoregressive processes

Statistics & Probability Letters, 2008

MSC: 62M10 62M20 62G15 62E20 a b s t r a c t In this paper the author considers an autoregressive... more MSC: 62M10 62M20 62G15 62E20 a b s t r a c t In this paper the author considers an autoregressive process where the parameters of the process are unknown and try to obtain pivots for predicting future observations. If we do a probabilistic prediction with the estimated model, where the parameters are estimated by a sample of size n, we introduce an error of order n −1 in the coverage probabilities of the prediction intervals. However we can reduce the order of the error if we calibrate adequately the estimated prediction bounds. The solution obtained can be expressed in terms of an approximate predictive pivot.

Research paper thumbnail of Intrinsic Analysis of Statistical Estimation

Annals of Statistics, 1995

Research paper thumbnail of Statistical Inference and Malliavin Calculus

Research paper thumbnail of Optimal investment in a Levy Market

The stock price process is modelled by a geometric Lévy process (taking into account jumps). Exce... more The stock price process is modelled by a geometric Lévy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However the model can be completed by the so called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.

Research paper thumbnail of Power variation of some integral long memory process

Research paper thumbnail of Additional utility of insiders with imperfect dynamical information

Finance and Stochastics, 2004

In this paper we consider a market driven by a Wiener process where there is an insider and a reg... more In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insider’s information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.

Research paper thumbnail of Optimal Investment in a Levy Market

Applied Mathematics and Optimization, 2006

In this paper we consider the optimal investment problem in a market where the stock price proces... more In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.

Research paper thumbnail of Dynamic complex hedging in additive markets

Quantitative Finance, 2010

In general, geometric additive models are incomplete and the perfect replication of derivatives, ... more In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity.

Research paper thumbnail of On the relationship between α connections and the asymptotic properties of predictive distributions

Bernoulli, 1999

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributi... more In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback±Leibler divergence as a loss function. He showed that estimative distributions with asymptotically ef®cient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between á connections and optimal predictive distributions. In particular, using an á divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to ácovariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Research paper thumbnail of A Characterization of Monotone and Regular Divergences

Annals of The Institute of Statistical Mathematics, 1998

In this paper we characterize the local structure of monotone and regular divergences, which incl... more In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Čencov, using the invariant properties of Amari's α-connections.

Research paper thumbnail of Approximate predictive pivots for autoregressive processes

Statistics & Probability Letters, 2008

MSC: 62M10 62M20 62G15 62E20 a b s t r a c t In this paper the author considers an autoregressive... more MSC: 62M10 62M20 62G15 62E20 a b s t r a c t In this paper the author considers an autoregressive process where the parameters of the process are unknown and try to obtain pivots for predicting future observations. If we do a probabilistic prediction with the estimated model, where the parameters are estimated by a sample of size n, we introduce an error of order n −1 in the coverage probabilities of the prediction intervals. However we can reduce the order of the error if we calibrate adequately the estimated prediction bounds. The solution obtained can be expressed in terms of an approximate predictive pivot.

Research paper thumbnail of Intrinsic Analysis of Statistical Estimation

Annals of Statistics, 1995

Research paper thumbnail of Statistical Inference and Malliavin Calculus

Research paper thumbnail of Optimal investment in a Levy Market

The stock price process is modelled by a geometric Lévy process (taking into account jumps). Exce... more The stock price process is modelled by a geometric Lévy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However the model can be completed by the so called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.

Research paper thumbnail of Power variation of some integral long memory process

Research paper thumbnail of Additional utility of insiders with imperfect dynamical information

Finance and Stochastics, 2004

In this paper we consider a market driven by a Wiener process where there is an insider and a reg... more In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insider’s information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.

Research paper thumbnail of Optimal Investment in a Levy Market

Applied Mathematics and Optimization, 2006

In this paper we consider the optimal investment problem in a market where the stock price proces... more In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.

Research paper thumbnail of Dynamic complex hedging in additive markets

Quantitative Finance, 2010

In general, geometric additive models are incomplete and the perfect replication of derivatives, ... more In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity.

Research paper thumbnail of On the relationship between α connections and the asymptotic properties of predictive distributions

Bernoulli, 1999

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributi... more In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback±Leibler divergence as a loss function. He showed that estimative distributions with asymptotically ef®cient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between á connections and optimal predictive distributions. In particular, using an á divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to ácovariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Research paper thumbnail of A Characterization of Monotone and Regular Divergences

Annals of The Institute of Statistical Mathematics, 1998

In this paper we characterize the local structure of monotone and regular divergences, which incl... more In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Čencov, using the invariant properties of Amari's α-connections.