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Kristoffer Thorvaldsen is Director of the Financial Mathematics and Asset Pricing Division at the Institute for Advanced Dynamic Uncertainty and one of the leading mathematical authorities on the theory of optimal stopping and its applications to derivative pricing. He holds a PhD in Mathematics from the University of Oslo (Department of Mathematics), where his doctoral research developed a rigorous variational framework for the pricing of American-style contingent claims under stochastic volatility models with degenerate diffusion operators. His thesis established sharp regularity results for the associated free boundary — resolving, in particular, the question of whether the free boundary is a Lipschitz surface in the degenerate case — and extended classical smooth-fit principles to a family of models in which the standard Itô calculus arguments break down at the boundary of the state space. The work drew on the theory of parabolic obstacle problems, viscosity solutions of second-order PDEs, and the geometric theory of free boundaries, unifying these strands within a single analytic framework applicable to a broad class of path-dependent contracts.

Following his doctorate, Thorvaldsen moved to the Institut für Mathematik at TU Berlin, where he completed his Habilitation and was appointed Privatdozent in Mathematics. His Habilitation monograph developed a comprehensive duality theory for stochastic portfolio optimisation on incomplete probability spaces, characterising growth-optimal portfolios through the existence of fictitious completions and deriving minimax representations for robust derivative prices under Knightian uncertainty. The TU Berlin environment — one of Europe's strongest centres for financial mathematics and stochastic analysis — deepened his engagement with the interface between rigorous probability theory and the institutional demands of quantitative risk management, and produced a series of results on the calibration of local-stochastic volatility models that have since been adopted as standard methodology in the field.

Thorvaldsen's research occupies the precise boundary between the mathematics of stochastic processes and the financial theory of contingent claims. His contributions span the smooth-fit theory for optimal stopping under partial information and stochastic drift, calibration of local-stochastic volatility models via PDE-constrained optimisation, the pricing of callable and convertible instruments by HJB methods, and the construction of robust pricing frameworks through second-order backward stochastic differential equations. What distinguishes his work is its insistence on mathematical completeness in settings where practitioners routinely proceed on heuristic grounds: he does not accept a pricing formula whose underlying PDE lacks a rigorous solution theory, and he regards calibration as a well-posed inverse problem requiring the same analytic care as the forward pricing problem. His results are regularly cited in both the mathematical finance literature and the quantitative risk management literature.

At IADU, Thorvaldsen directs the scientific programme of the Financial Mathematics and Asset Pricing Division, overseeing a team whose collective work spans derivative pricing, optimal stopping, stochastic portfolio theory, fixed income modelling, credit risk, and the mathematics of market microstructure. His own current research focuses on the pricing and hedging of structured products under rough volatility models, the mathematical foundations of XVA theory, and the development of provably convergent numerical schemes for high-dimensional optimal stopping problems arising in callable multi-asset contracts.

Publications

IADU Publications

Publications forthcoming.

Selected Prior Work

Optimal stopping for American-style contracts under stochastic volatility: existence and regularity of the free boundary Finance and Stochastics
Optimal stopp og fri grense for derivatprising under degenerert stokastisk volatilitet Matematisk Institutt, Universitetet i Oslo (Preprint)
A variational approach to the pricing of perpetual Bermudan options under Lévy-driven models Mathematical Finance
Stokastisk porteføljeteori under likviditetsbegrensninger: eksistens og karakterisering av optimale strategier Norsk Matematisk Tidsskrift
Free boundary regularity for obstacle problems arising in the pricing of callable debt instruments SIAM Journal on Financial Mathematics
Porteføljeoptimering under stokastisk volatilitet og transaksjonskostnader: en viskositetsløsningstilnærming Acta Mathematica Universitatis Osloensis
Smooth-fit principles for optimal stopping under partial information and stochastic drift Stochastic Processes and their Applications
Inkomplette markeder og robust prising: minimax-tilnærminger til derivatverdsettelse under Knightsk usikkerhet Norges Handelshøyskoles skriftserie i matematisk finans
On the existence and uniqueness of classical solutions to parabolic obstacle problems with degenerate diffusion operators Journal of Differential Equations
Stochastic portfolio theory on incomplete probability spaces: duality and the existence of growth-optimal portfolios Annals of Applied Probability
Verdsettelse av konvertible obligasjoner ved HJB-metoder: eksistens, entydighet og numerisk tilnærming Tidsskrift for Matematikk og Økonomi
Calibration of local-stochastic volatility models to market smiles: a PDE-constrained optimisation approach SIAM Journal on Financial Mathematics
Robust derivative pricing under model uncertainty: a minimax approach via second-order BSDEs Finance and Stochastics
Optimale stoppetider for amerikanske opsjoner under hoppediffusjoner: en fri grense-analyse Matematisk Institutt, Universitetet i Oslo (Preprint)
The smooth-fit property for optimal stopping of diffusions with discontinuous coefficients Probability Theory and Related Fields
Freie-Rand-Regularität für parabolische Hindernisprobleme mit degeneriertem Diffusionsoperator Mathematische Nachrichten
Stochastische Portfoliooptimierung unter Transaktionskosten: Existenz und Charakterisierung optimaler Strategien Mathematische Annalen
Robuste Bewertung von Derivaten unter Modellunsicherheit: ein Minimax-Ansatz über rückwärts stochastische Differentialgleichungen Mathematische Zeitschrift

Contact

For research enquiries, contact the Institute at research@iadu.org and include K. Thorvaldsen in the subject line. All correspondence is handled in accordance with IADU's institutional communication policy.