A note on utility based pricing and asymptotic risk diversification

In principle, liabilities combining both insurancial risks (e.g. mortality/longevity, crop yield,...) and pure financial risks cannot be priced neither by applying the usual actuarial principles of diversification, nor by arbitrage-free replication arguments. Still, it has been often proposed in the literature to combine these two approaches by suggesting to hedge a pure financial payoff computed by taking the mean under the historical/objective probability measure on the part of the risk that can be diversified. Not surprisingly, simple examples show that this approach is typically inconsistent for risk adverse agents. We show that it can nevertheless be recovered asymptotically if we consider a sequence of agents whose absolute risk aversions go to zero and if the number of sold claims goes to infinity simultaneously. This follows from a general convergence result on utility indifference prices which is valid for both complete and incomplete financial markets. In particular, if the underlying financial market is complete, the limit price corresponds to the hedging cost of the mean payoff. If the financial market is incomplete but the agents behave asymptotically as exponential utility maximizers with vanishing risk aversion, we show that the utility indifference price converges to the expectation of the discounted payoff under the minimal entropy martingale measure.     

Photosubstitution in a trisheteroleptic ruthenium complex inhibits conjunctival melanoma growth in a zebrafish orthotopic xenograft model

In vivo data are rare but essential for establishing the clinical potential of ruthenium-based photoactivated chemotherapy (PACT) compounds, a new family of phototherapeutic drugs that are activated via ligand photosubstitution. Here a novel trisheteroleptic ruthenium complex [Ru(dpp)(bpy)(mtmp)](PF₆)₂ ([2](PF₆)₂, dpp = 4,7-diphenyl-1,10-phenanthroline, bpy = 2,2′-bipyridine, mtmp = 2-methylthiomethylpyridine) was synthesized and its light-activated anticancer properties were validated in cancer cell monolayers, 3D tumor spheroids, and in embryonic zebrafish cancer models. Upon green light irradiation, the non-toxic mtmp ligand is selectively cleaved off, thereby releasing a phototoxic ruthenium-based photoproduct capable notably of binding to nuclear DNA and triggering DNA damage and apoptosis within 24–48 h. In vitro, fifteen minutes of green light irradiation (21 mW cm⁻², 19 J cm⁻², 520 nm) were sufficient to generate high phototherapeutic indexes (PI) for this compound in a range of cancer cell lines including lung (A549), prostate (PC3Pro4), conjunctival melanoma (CRMM1, CRMM2, CM2005.1) and uveal melanoma (OMM1, OMM2.5, Mel270) cancer cell lines. The therapeutic potential of [2](PF₆)₂ was further evaluated in zebrafish embryo ectopic (PC3Pro4) or orthotopic (CRMM1, CRMM2) tumour models. The ectopic model consisted of red fluorescent PC3Pro4-mCherry cells injected intravenously (IV) into zebrafish, that formed perivascular metastatic lesions at the posterior ventral end of caudal hematopoietic tissue (CHT). By contrast, in the orthotopic model, CRMM1- and CRMM2-mCherry cells were injected behind the eye where they developed primary lesions. The maximally-tolerated dose (MTD) of [2](PF₆)₂ was first determined for three different modes of compound administration: (i) incubating the fish in prodrug-containing water (WA); (ii) injecting the prodrug intravenously (IV) into the fish; or (iii) injecting the prodrug retro-orbitally (RO) into the fish. To test the anticancer efficiency of [2](PF₆)₂, the embryos were treated 24 h after engraftment at the MTD. Optimally, four consecutive PACT treatments were performed on engrafted embryos using 60 min drug-to-light intervals and 90 min green light irradiation (21 mW cm⁻², 114 J cm⁻², 520 nm). Most importantly, this PACT protocol was not toxic to the zebrafish. In the ectopic prostate tumour models, where [2](PF₆)₂ showed the highest photoindex in vitro (PI > 31), the PACT treatment did not significantly diminish the growth of primary lesions, while in both conjunctival melanoma orthotopic tumour models, where [2](PF₆)₂ showed more modest photoindexes (PI ∼ 9), retro-orbitally administered PACT treatment significantly inhibited growth of the engrafted tumors. Overall, this study represents the first demonstration in zebrafish cancer models of the clinical potential of ruthenium-based PACT, here against conjunctival melanoma.

A new tris-heteroleptic photoactivated chemotherapy ruthenium complex induces apoptosis upon green light activation in a zebrafish orthothopic conjunctival melanoma xenograft model.     

Post-Modification of Copolymers Obtained by ATRP for an Application in Heterogeneous Asymmetric Salen Catalysis

Copolymers are valuable supports for obtaining heterogeneous catalysts that allow their recycling and therefore substantial savings, particularly in the field of asymmetric catalysis. This contribution reports the use of two comonomers: Azido-3-propylmethacrylate (AZMA) bearing a reactive azide function was associated with 2-methoxyethyl methacrylate (MEMA), used as a spacer, for the ATRP synthesis of copolymers, and then post-functionalized with a propargyl chromium salen complex. The controlled homopolymerization of MEMA by ATRP was firstly described and proved to be more controlled in molar mass than that of AZMA for conversions up to 63%. The ATRP copolymerization of both monomers made it possible to control the molar masses and the composition, with nevertheless a slight increase in the dispersity (from 1.05 to 1.3) when the incorporation ratio of AZMA increased from 10 to 50 mol%. These copolymers were post-functionalized with chromium salen units by click chemistry and their activity was evaluated in the asymmetric ring opening of cyclohexene oxide with trimethylsilyl azide. At an equal catalytic ratio, a significant increase in enantioselectivity was obtained by using the copolymer containing the largest part of salen units, probably allowing, in this case, the more favorable bimetallic activation of both the engaged nucleophile and electrophile. Moreover, the catalytic polymer was recovered by simple filtration and re-engaged in subsequent catalytic runs, up to seven times, without loss of activity or selectivity.     

Circularly Polarized Luminescence from Cyclic (Alkyl)(Amino) Carbene Derived Propellers

Organic circularly polarized luminescence (CPL)-active molecular emitters featuring dynamic propeller-like luminophores were prepared in one step from cyclic(alkyl)(amino) carbenes (CAACs). These molecules exhibit through-space arene-arene π-delocalization and rapid intramolecular inter-system crossing (ISC) in line with their helical character.     

Numerical methods for control-based continuation of relaxation oscillations

Nonlinear Dynamics - Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of...