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- Title
- DYNAMIC CONIC FINANCE: NO-ARBITRAGE PRICING AND NO-GOOD-DEAL PRICING FOR DIVIDEND-PAYING SECURITIES IN DISCRETE-TIME MARKETS WITH TRANSACTION COSTS
- Creator
- Rodriguez, Rodrigo
- Date
- 2012-06-27, 2012-07
- Description
-
This thesis studies no-arbitrage pricing and dynamic conic nance for dividend-paying securities in discrete-time markets with transaction...
Show moreThis thesis studies no-arbitrage pricing and dynamic conic nance for dividend-paying securities in discrete-time markets with transaction costs. The rst part investigates no-arbitrage pricing for dividend-paying securities in discrete-time markets with transaction costs. We introduce the value process and the self- nancing condition in our context. Then, we prove a version of First Fundamental Theorem of Asset Pricing. Speci cally, we prove that the no-arbitrage condition under the e cient friction assumption is equivalent to the existence of a risk-neutral measure. We formulate an appropriate notion of a consistent pricing system in our set-up, and we prove that if there are no transaction costs on the dividends paid by the securities, then the no-arbitrage condition under the e cient friction assumption is equivalent to the existence of a consistent pricing system. We nish the chapter by deriving dual representations for the superhedging ask price and subhedging bid price of a derivative contract. The second part studies dynamic conic nance in the set-up introduced in the rst part. We formulate the no-good-deal condition in terms of a family of dynamic coherent risk measures, and then we prove a version of the Fundamental Theorem of No-Good-Deal Pricing. The Fundamental Theorem of No-Good-Deal Pricing provides a necessary and su cient condition for the no-good-deal condition to hold. Next, we study the no-good-deal ask and bid prices of a derivative contract. We particularize our results to the dynamic Gain-Loss Ratio, and compute the no-good-deal prices of European-style Asian options in a market with transaction costs.
Ph.D. in Applied Mathematics, July 2012
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- Title
- DYNAMIC CONIC FINANCE VIA BACKWARD STOCHASTIC DIFFERENCE EQUATIONS AND RECURSIVE CONSTRUCTION OF CONFIDENCE REGIONS
- Creator
- Chen, Tao
- Date
- 2016, 2016-07
- Description
-
This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics. The contribution to...
Show moreThis thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics. The contribution to mathematical finance is made via developing new theoretical results in the area of conic finance. Specifically, we have advanced dynamic aspects of conic finance by developing an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities using the theory of dynamic acceptability indices. This has been done within the framework of general probability spaces and discrete time. In the process, we have advanced the theory of dynamic sub-scale invariant performance measures. In particular, we proved a representation theorem of such measures in terms of a family of dynamic convex risk measures, and provided a representation of dynamic risk measures in terms of BS Es. The contribution to statistics is of fundamental importance as it initiates the theory underlying recursive computation of confidence regions for finite dimensional parameters in the context of stochastic dynamical systems. In the field of engineering, particularly in the field of control engineering, the area of recursive point estimation came to great prominence in the last forty years. However, there has been no work done with regard to recursive computation of confidence regions. To partially fill this gap, the second part of the thesis is devoted to recursive construction of confidence regions for parameters characterizing the one-step transition kernel of a time-homogeneous Markov chain.
Ph.D. In Applied Mathematics, July 2016
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- Title
- MONTE CARLO SIMULATION OF INFINITE-DIMENSIONAL INTEGRALS
- Creator
- Niu, Ben
- Date
- 2011-04-13, 2011-05
- Description
-
This thesis is motivated by pricing a path-dependent financial derivative, such as an Asian option, which requires the computation of the...
Show moreThis thesis is motivated by pricing a path-dependent financial derivative, such as an Asian option, which requires the computation of the expectation of a payoff function, which depends on a Brownian motion. Employing a standard series expansion of the Brownian motion, the latter problem is equivalent to the computation of the expectation of a function of the corresponding i.i.d. sequence of random coefficients. This motivates the construction and the analysis of algorithms for numerical integration with respect to a product probability measure on the infinite-dimensional sequence. The class of integrands studied in this thesis resides in the unit ball in a reproducing kernel Hilbert space obtained by superposition of weighted tensor product spaces of functions of finitely many variables. Combining tractability results for high-dimensional integration with the multi-level technique we obtain new algorithms for infinite-dimensional integration. These deterministic multi-level algorithms use variable subspace sampling and they are superior to any deterministic algorithm based on fixed subspace sampling with respect to the respective worst case error. Numerical experiment results are presented at the end.
Ph.D. in Applied Mathematics, May 2011
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- Title
- A NUMERICAL AND ANALYTICAL STUDY OF THE GROWTH OF SECOND PHASE PARTICLES USING A SHARP INTERFACE APPROACH
- Creator
- Barua, Amlan K.
- Date
- 2012-08-15, 2012-12
- Description
-
Two phase alloys are quite important in materials science and metallurgy. Some common examples include nickel-aluminum system, iron-carbon...
Show moreTwo phase alloys are quite important in materials science and metallurgy. Some common examples include nickel-aluminum system, iron-carbon system etc. The most important macroscopic properties of these alloys depend on size, orientation and concentration of the second-phase precipitates. It is necessary to understand the details of formation, growth and equilibrium conditions of these micro-structures for better material production. In this dissertation we investigate the growth of the precipitates within the matrix using a sharp interface approach. We consider the effects of elastic fields on the evolution of the precipitates. The elastic fields can either be applied at the far field or can simply arise as a result of crystallographic difference between matrix and precipitate phase. The precipitates exhibit complicated morphology because of the Mullins-Sekerka instability. Our investigation is based on both analytical and numerical techniques. We use linear analysis to understand the qualitative behavior of the problem, at least for short time. To simulate the long time dynamics of the problem and to understand the effects of nonlinearity, we use highly accurate boundary integral methods. Our main contribution in this thesis is threefold. First, starting from linear analysis, we focus on the conditions under which stable growth, in presence of elastic field, is possible for a single precipitate. Finding such conditions are important in material production and simple conditions like constant material flux and constant elastic fields produce precipitates with complicated shapes. Second, we propose a space-time rescaling of the original boundary integral equations of the problem. The rescaling enables us to accurately simulate very long time behavior of the system comprising of multiple precipitates growing under different mass flux and elasticity. It also helps us to understand the long time interaction of precipitates. Third, we xiii implement an adaptive treecode to reduce the computational complexity of the iterative solver from O(N2) to O(N logN) where N is the dimension of the discrete problem. The efficiency of the treecode is demonstrated by performing simulations. Also a parallelization strategy for the treecode is discussed. The speed-up from the parallelization is demonstrated using moderate number of cores. xiv
PH.D in Applied Mathematics, December 2012
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- Title
- Algorithms for Discrete Data in Statistics and Operations Research
- Creator
- Schwartz, William K.
- Date
- 2021-11-19, 2021-12
- Publisher
- ProQuest, https://www.proquest.com/docview/2622985712
- Description
-
Sponsorship: The Air Force Office of Scientific Research's grant FA9550-14-1-0141 supported Prof. Petrović's and my initial work on this project.