We introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are neither semimartingales, nor Markov processes in general. We provide explicit exponential-affine representations of the Fourier-Laplace functional in terms of the solution of an associated system of deterministic integral equations, extending well-known formulas for classical affine diffusions. For specific state spaces, we prove existence, uniqueness, and invariance properties of solutions of the corresponding stochastic convolution equations. Our arguments avoid infinite-dimensional stochastic analysis as well as stochastic integration with respect to non-semimartingales, relying instead on tools from the theory of finite-dimensional deterministic convolution equations. Our findings generalize and clarify recent results in the literature on rough volatility models in finance.

Human NAD(P)H:quinone oxidoreductase 1 (NQO1) is essential for the antioxidant defense system, stabilization of tumor suppressors (e.g. p53, p33, and p73), and activation of quinone-based chemotherapeutics. Overexpression of NQO1 in many solid tumors, coupled with its ability to convert quinone-based chemotherapeutics into potent cytotoxic compounds, have made it a very attractive target for anticancer drugs. A naturally occurring single-nucleotide polymorphism (C609T) leading to an amino acid exchange (P187S) has been implicated in the development of various cancers and poor survival rates following anthracyclin-based adjuvant chemotherapy. Despite its importance for cancer prediction and therapy, the exact molecular basis for the loss of function in NQO1 P187S is currently unknown. Therefore, we solved the crystal structure of NQO1 P187S. Surprisingly, this structure is almost identical to NQO1. Employing a combination of NMR spectroscopy and limited proteolysis experiments, we demonstrated that the single amino acid exchange destabilized interactions between the core and C-terminus, leading to depopulation of the native structure in solution. This collapse of the native structure diminished cofactor affinity and led to a less competent FAD-binding pocket, thus severely compromising the catalytic capacity of the variant protein. Hence, our findings provide a rationale for the loss of function in NQO1 P187S with a frequently occurring single-nucleotide polymorphism.

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Recent studies revealed that mitochondrial Ca2+ channels, which control energy flow, cell signalling and death, are macromolecular complexes that basically consist of the pore-forming mitochondrial Ca2+ uniporter (MCU) protein, the essential MCU regulator (EMRE), and the mitochondrial Ca2+ uptake 1 (MICU1). MICU1 is a regulatory subunit that shields mitochondria from Ca2+ overload. Before the identification of these core elements, the novel uncoupling proteins 2 and 3 (UCP2/3) have been shown to be fundamental for mitochondrial Ca2+ uptake. Here we clarify the molecular mechanism that determines the UCP2/3 dependency of mitochondrial Ca2+ uptake. Our data demonstrate that mitochondrial Ca2+ uptake is controlled by protein arginine methyl transferase 1 (PRMT1) that asymmetrically methylates MICU1, resulting in decreased Ca2+ sensitivity. UCP2/3 normalize Ca2+ sensitivity of methylated MICU1 and, thus, re-establish mitochondrial Ca2+ uptake activity. These data provide novel insights in the complex regulation of the mitochondrial Ca2+ uniporter by PRMT1 and UCP2/3.

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We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best of our knowledge, this is the first study that proves such (global) uniqueness result for a system of fully coupled quadratic BSDEs.

This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker.In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims. This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Applied Probability, 2014, Vol. 24, No. 1, 54-75. This reprint differs from the original in pagination and typographic detail. 1 2 S. PULIDO [4,5]. Additionally, in markets such as commodity markets and the housing market, primary securities such as mortgages cannot be sold short because they cannot be borrowed. This paper aims to understand the consequences of short sales prohibition in semimartingale financial models. The fundamental theorem of asset pricing establishes the equivalence between the absence of arbitrage, a key concept in mathematical finance, and the existence of a probability measure under which the asset prices in the market have a characteristic behavior. In Section 3, we prove the fundamental theorem of asset pricing in continuous time financial models with short sales prohibition where prices are driven by locally bounded semimartingales. This extends related results by Jouini and Kallal in [23], Schürger in [34], Frittelli in [18], Pham and Touzi in [30], Napp in [29] and more recently by Karatzas and Kardaras in [26] to the framework of the seminal work of Delbaen and Schachermayer in [9].Additionally, the hedging problem of contingent claims in markets with convex portfolio constraints where prices are driven by diffusions and discrete processes has been extensively studied; see [6], Chapter 5 of [27] and Chapter 9 of [17]. In Section 4, inspired by the works of Jacka in [19] and Ansel and Stricker in [1], and using ideas from [16], we extend some of these classical results to more general semimartingale financial models. We also reveal an interesting financial connection to the concept of maximal claims, first introduced by Delbaen and Schachermayer in [9] and [10].