The Søren Kierkegaard Research Centre

Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomi...

Quantitative Finance Research Centre Quantitative F Inance Research Centre Quantitative Finance Research Centre

In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993) type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito’s lemma. An integral expression for the general solution of the PDE is presented b...

Quantitative Finance Research Centre Quantitative F Inance Research Centre

Kierkegaard , Socrates and Existential Individuality

The 19 century Danish philosopher Søren Kierkegaard was a profoundly religious thinker. He is also regarded as the father of Existentialism, one of the most important philosophical movements of the 20 century. The term ‘existentialist’ is applied to those philosophers, like Jean-Paul Sartre and Albert Camus, who held that the foundation of all philosophical thought is to be found in the actual,...

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