This thesis presents the main results of my research in the field of computational finance and portfolios optimization. We focus on pricing Asian basket options and portfolio problems in the presence of inflation with stochastic interest rates.<p><p>In Chapter 2, we concentrate upon the derivation of bounds for European-style discrete arithmetic Asian basket options in a Black and Scholes framework.We start from methods used for basket options and Asian options. First, we use the general approach for deriving upper and lower bounds for stop-loss premia of sums of non-independent random variables as in Kaas et al. [Upper and lower bounds for sums of random variables, Insurance Math. Econom. 27 (2000) 151–168] or Dhaene et al. [The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom. 31(1) (2002) 3–33]. We generalize the methods in Deelstra et al. [Pricing of arithmetic basket options by conditioning, Insurance Math. Econom. 34 (2004) 55–57] and Vanmaele et al. [Bounds for the price of discrete sampled arithmetic Asian options, J. Comput. Appl. Math. 185(1) (2006) 51–90]. Afterwards we show how to derive an analytical closed-form expression for a lower bound in the non-comonotonic case. Finally, we derive upper bounds for Asian basket options by applying techniques as in Thompson [Fast narrow bounds on the value of Asian options, Working Paper, University of Cambridge, 1999] and Lord [Partially exact and bounded approximations for arithmetic Asian options, J. Comput. Finance 10 (2) (2006) 1–52]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and time-to-maturity<p><p>In Chapter 3, we propose some moment matching pricing methods for European-style discrete arithmetic Asian basket options in a Black & Scholes framework. We generalize the approach of Curran M. (1994) [Valuing Asian and portfolio by conditioning on the geometric mean price”, Management science, 40, 1705-1711] and of Deelstra G. Liinev J. and Vanmaele M. (2004) [Pricing of arithmetic basket options by conditioning”, Insurance: Mathematics & Economics] in several ways. We create a framework that allows for a whole class of conditioning random variables which are normally distributed. We moment match not only with a lognormal random variable but also with a log-extended-skew-normal random variable. We also improve the bounds of Deelstra G. Diallo I. and Vanmaele M. (2008). [Bounds for Asian basket options”, Journal of Computational and Applied Mathematics, 218, 215-228]. Numerical results are included and on the basis of our numerical tests, we explain which method we recommend depending on moneyness and<p>time-to-maturity.<p><p>In Chapter 4, we use the stochastic dynamic programming approach in order to extend<p>Brennan and Xia’s unconstrained optimal portfolio strategies by investigating the case in which interest rates and inflation rates follow affine dynamics which combine the model of Cox et al. (1985) [A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), 385-408] and the model of Vasicek (1977) [An equilibrium characterization of the term structure, Journal of Financial Economics, 5, 177-188]. We first derive the nominal price of a zero coupon bond by using the evolution PDE which can be solved by reducing the problem to the solution of three ordinary differential equations (ODE). To solve the corresponding control problems we apply a verification theorem without the usual Lipschitz assumption given in Korn R. and Kraft H.(2001)[A Stochastic control approach to portfolio problems with stochastic interest rates, SIAM Journal on Control and Optimization, 40(4), 1250-1269] or Kraft(2004)[Optimal Portfolio with Stochastic Interest Rates and Defaultable Assets, Springer, Berlin].<p><p><p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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Face à l’instabilité des cours agricoles et à ses conséquences notamment pour les pays en développement, la première partie de cette thèse est consacrée à la présentation des déterminants des cours des matières premières alimentaires, incluant les évolutions récentes en matière d’offre, en tenant compte des conséquences du réchauffement climatique, et de demande, considérant notamment les biocarburants. Il est également question de présenter la financiarisation en cours des économies, et les doutes qui planent sur le rôle que peuvent avoir la spéculation sur les marchés à terme ou encore la mise en œuvre des politiques monétaires, sur les cours au comptant observés sur les marchés physiques des produits agricoles. Suite aux réflexions et éléments de littérature avancés, la seconde partie procède de deux études empiriques. La première est axée sur l’impact de la spéculation sur les marchés financiers à terme sur le cours des sous-jacents (agricoles), alors que la seconde questionne le rôle des marchés monétaires, abordé à travers la capacité du banquier central à stabiliser les taux d’intérêt à court terme. Sur cette base, des conclusions mais également des pistes de recherche sont établies, du fait du prolongement en cours du processus de financiarisation des économies. / Faced with instability of agricultural commodities’ prices and its consequences especially for developing countries, the first part of this thesis is devoted to the presentation of food commodities’ prices, including recent developments with respect to the offering, taking into account the consequences of global warming and demand, as well as the importance of biofuels. It is also question to present the financialization of economies, and the doubts that take over the role of speculation on the futures markets or the implementation of monetary policies, on the spot prices observed on physical agricultural commodities markets. Following the advanced literature reflections and elements, the second part proceeds of two empirical studies, the first one focused on the impact of speculation about the financial futures markets on the underlying asset’s price (agricultural), while the second one examines the role of money markets through the capacities of the central banker to stabilize short-term interest rates. On this basis, conclusions but also future research are established due to the continuation of the economies financialization process.