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• 1.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Weather derivatives pricing using regim switching models2017Report (Other academic)

In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with mean different from zero. We develop the mathematical formulas for pricing futures contract on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. We also present the mathematical expressions for pricing the corresponding options on futures contracts for the same temperature indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We provide the description of Montecarlo simulation method for pricing weather derivatives under this model and use it to price a few weather derivatives call option contracts.

• 2.
Linköping University, Department of Mathematics, Mathematical Statistics .
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Weather Derivatives Pricing Using Regime Switching Model2018In: Monte Carlo Methods and Applications, ISSN 0929-9629, Vol. 24, no 1, p. 13-27Article in journal (Refereed)

In this study we discuss the pricing of weather derivatives whose underlying weather variable is temperature. The dynamics of temperature in this study follows a two state regime switching model with a heteroskedastic mean reverting process as the base regime and a shifted regime defined by Brownian motion with nonzero drift. We develop mathematical formulas for pricing futures and option contracts on heating degree days (HDDs), cooling degree days (CDDs) and cumulative average temperature (CAT) indices. The local volatility nature of the model in the base regime captures very well the dynamics of the underlying process, thus leading to a better pricing processes for temperature derivatives contracts written on various index variables. We use the Monte Carlo simulation method for pricing weather derivatives call option contracts.

• 3.
University of Idaho.
Blåeldsvägen 12B, Sturefors, Sweden. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Conditional persistence of Gaussian random walks2014In: Electronic Communications in Probability, ISSN 1083-589X, E-ISSN 1083-589X, Vol. 19, no 70, p. 1-9Article in journal (Refereed)

Let $\{X_n\}_{n\geq1}$ be a sequence of i.i.d. standard Gaussian random variables, let $S_n=\sum_{i=1}^nX_i$ be the Gaussian random walk, and let $T_n=\sum_{i=1}^nS_i$ be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence:\begin{align*}\mathbb{P}\left\{\max_{1\leq k \leq n}T_{k} \leq 0\,\,\Big|\,\,T_n=0,S_n=0\right\}&\lesssim n^{-1/2},\\\mathbb{P}\left\{\max_{1\leq k \leq 2n}T_{k} \leq 0\,\,\Big|\,\,T_{2n}=0,S_{2n}=0\right\}&\gtrsim\frac{n^{-1/2}}{\log n},\end{align*}for $n\rightarrow\infty,$ which partially proves a conjecture by Caravenna and Deuschel (2008).

• 4.
Univ Idaho, Dept Math, Moscow, ID 83844 USA.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Upper tail probabilities of integrated Brownian motions2015In: Science China Mathematics, ISSN 1674-7283, Vol. 58, no 5, p. 1091-1100Article in journal (Refereed)

We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the L (p) norm. For the uniform norm, Talagrands approach is used, while for the L (p) norm, Zolotares approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities (large ball probabilities) for general Gaussian random variables in Banach spaces. As applications, explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.

• 5.
Uppsala University, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
LAPLACE TRANSFORM ASYMPTOTICS AND LARGE DEVIATION PRINCIPLES FOR LONGEST SUCCESS RUNS IN BERNOULLI TRIALS2016In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 3, p. 747-764Article in journal (Refereed)

The longest stretch L(n) of consecutive heads in n independent and identically distributed coin tosses is seen from the prism of large deviations. We first establish precise asymptotics for the moment generating function of L(n) and then show that there are precisely two large deviation principles, one concerning the behavior of the distribution of L(n) near its nominal value log(1/p) n and one away from it. We discuss applications to inference and to logarithmic asymptotics of functionals of L(n).

• 6.
Guangzhou University, Peoples R China.
South China University of Technology, Peoples R China. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
On the longest block in Luroth expansion2018In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, no 1, p. 522-532Article in journal (Refereed)

In this paper, for a finite subset A subset of {2,3, center dot center dot center dot }, we introduce the notion of longest block function L-n (x,A) for the Luroth expansion of x epsilon [0,1) with respect to A and consider the asymptotic behavior of L-n (x,A) as n tends to infinity. We also obtain the Hausdorff dimensions of the level sets and exceptional set arising from the longest block function. (c) 2017 Elsevier Inc. All rights reserved.

• 7.
Guangzhou Univ, Peoples R China.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
On longest matching consecutive subsequence2019In: International Journal of Number Theory, ISSN 1793-0421, Vol. 15, no 8, p. 1745-1758Article in journal (Refereed)

The longest matching consecutive subsequence between two N-ary expansions found applications in information theory and molecular biology. In this paper, we establish an almost sure limit theorem for the longest matching consecutive subsequence, and investigate the size of the set of points violating the limit in terms of Hausdorff dimension.

• 8.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Ningbo University of Technology, Peoples R China. Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
A Gaussian expectation product inequality2017In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 124Article in journal (Refereed)

Let (X-1,. . ., X-n) be any n-dimensional centered Gaussian random vector, in this note the following expectation product inequality is proved: E Pi (n)(j=1) f(j)( X-j) amp;gt;= Pi (n)(j=1) Ef(j)(X-j) for functionsh, 1 amp;lt;= j amp;lt;= n, taking the forms f(j)(x) = integral(infinity)(0) where mu(j), 1 amp;lt;= j amp;lt;= n, are finite positive measures. The motivation of studying such an inequality comes from the Gaussian correlation conjecture (which was recently proved) and the Gaussian moment product conjecture (which is still unsolved). Several explicit examples of such functions f(j) are given. The proof is built on characteristic functions of Gaussian random variables. (C) 2017 Elsevier B.V. All rights reserved.

• 9.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
A general large deviation principle for longest runs2016In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 110, p. 128-132Article in journal (Refereed)

In this note we prove a general large deviation principle (LDP) for the longest success run in a sequence of independent Bernoulli trails. This study not only recovers several recently derived LDPs, but also gives new LDPs for the longest success run. The method is based on the Bryc’s inverse Varadhan lemma, which can be intuitively generalized to the longest success run in a two-state (success and failure) Markov chain.

• 10.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
ON THE LONGEST RUNS IN MARKOV CHAINS2018In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 38, no 2, p. 407-428Article in journal (Refereed)

In the first n steps of a two-state (success and failure) Markov chain, the longest success run L(n) has been attracting considerable attention due to its various applications. In this paper, we study L(n) in terms of its two closely connected properties: moment generating function and large deviations. This study generalizes several existing results in the literature, and also finds an application in statistical inference. Our method on the moment generating function is based on a global estimate of the cumulative distribution function of L(n) proposed in this paper, and the proofs of the large deviations include the Gartner-Ellis theorem and the moment generating function.

• 11.
Blåeldsvägen 12B, Sturefors, Sweden.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Probabilities of hitting a convex hull2014In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 352, no 11, p. 935-940Article in journal (Refereed)

In this note, we consider the non-negative least-square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull.

• 12.
Nanyang Technological University.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. Universidade de Lisboa.
Feynman-Kac formula for Levy processesand semiclassical (Euclidean) momentum representation2014In: Markov Processes and Related Fields, ISSN 1024-2953, Vol. 20, no 3, p. 577-600Article in journal (Refereed)

We prove a version of the Feynman-Kac formula for Levy processes andintegro-differential operators, with application to the momentum representationof suitable quantum (Euclidean) systems whose Hamiltonians involve L´evytypepotentials. Large deviation techniques are used to obtain the limitingbehavior of the systems as the Planck constant approaches zero. It turns outthat the limiting behavior coincides with fresh aspects of the semiclassical limitof (Euclidean) quantum mechanics. Non-trivial examples of Levy processes areconsidered as illustrations and precise asymptotics are given for the terms inboth configuration and momentum representations.

• 13.
School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. Group of Mathematical Physics, University of Lisbon, Lisbon, Portugal.
Large deviations for Bernstein bridges2016In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 126, no 5, p. 1285-1305Article in journal (Refereed)

Bernstein processes over a finite time interval are simultaneously forward and backward Markov processes with arbitrarily fixed initial and terminal probability distributions. In this paper, a large deviation principle is proved for a family of Bernstein processes (depending on a small parameter ħ which is called the Planck constant) arising naturally in Euclidean quantum physics. The method consists in nontrivial Girsanov transformations of integral forms, suitable equivalence forms for large deviations and the (local and global) estimates on the parabolic kernel of the Schrödinger operator.

• 14.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Asymptotic expansions for Laplace transforms of Markov processes2018In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, no 1, p. 694-721Article in journal (Refereed)

Let mu(epsilon) be the probability measures on D[0,T] of suitable Markov processes {xi(epsilon)(t)}0 amp;lt;= t amp;lt;= T (possibly with small jumps) depending on a small parameter epsilon amp;gt;0, where D[0,T] denotes the space of all functions on [0, T] which are right continuous with left limits. In this paper we investigate asymptotic expansions for the Laplace transforms integral(D[0,T]) exp{epsilon F-1(x)}mu(epsilon)(dx) as epsilon -amp;gt; 0 for smooth functionals F on D[0,T]. This study not only recovers several well-known results, but more importantly provides new expansions for jump Markov processes. Besides several standard tools such as exponential change of measures and Taylors expansions, the novelty of the proof is to implement the expectation asymptotic expansions on normal deviations which were recently derived in [13]. (c) 2017 Elsevier Inc. All rights reserved.

• 15.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Exact upper tail probabilities of random series2015In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 99, p. 13-19Article in journal (Refereed)

In this paper, we obtain new estimates on upper tail probabilities of suitable random series involving a distribution having an exponential tail. These estimates are exact, and the distribution is not heavy-tailed.

• 16.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Large deviations for Markov bridges with jumps2014In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 416, no 1, p. 1-12Article in journal (Refereed)

In this paper, we consider a family of Markov bridges with jumps constructed from truncated stable processes. These Markov bridges depend on a small parameter h greater than 0, and have fixed initial and terminal positions. We propose a new method to prove a large deviation principle for this family of bridges based on compact level sets, change of measures, duality and various global and local estimates of transition densities for truncated stable processes.

• 17.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
On the large deviation principle of generalized Brownian bridges2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 430, no 2, p. 845-856Article in journal (Refereed)

In this paper we consider a family of generalized Brownian bridges with a small noise, which was used by Brennan and Schwartz [3] to model the arbitrage profit in stock index futures in the absence of transaction costs. More precisely, we study the large deviation principle of these generalized Brownian bridges as the noise becomes infinitesimal. (C) 2015 Elsevier Inc. All rights reserved.

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