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  1. ; ; ; ; ; ; ; ; ; ( , Magnetic Resonance in Medicine)
    Abstract Purpose

    The interaction between129Xe atoms and pulmonary capillary red blood cells provides cardiogenic signal oscillations that display sensitivity to precapillary and postcapillary pulmonary hypertension. Recently, such oscillations have been spatially mapped, but little is known about optimal reconstruction or sensitivity to artifacts. In this study, we use digital phantom simulations to specifically optimize keyhole reconstruction for oscillation imaging. We then use this optimized method to re‐establish healthy reference values and quantitatively evaluate microvascular flow changes in patients with chronic thromboembolic pulmonary hypertension (CTEPH) before and after pulmonary thromboendarterectomy (PTE).

     Methods

    A six‐zone digital lung phantom was designed to investigate the effects of radial views, key radius, and SNR. One‐point Dixon129Xe gas exchange MRI images were acquired in a healthy cohort (n = 17) to generate a reference distribution and thresholds for mapping red blood cell oscillations. These thresholds were applied to 10 CTEPH participants, with 6 rescanned following PTE.

     Results

    For undersampled acquisitions, a key radius of was found to optimally resolve oscillation defects while minimizing excessive heterogeneity. CTEPH participants at baseline showed higher oscillation defect + low (32 ± 14%) compared with healthy volunteers (18 ± 12%,p < 0.001). For those scanned both before and after PTE, oscillation defect + low decreased from 37 ± 13% to 23 ± 14% (p = 0.03).

     Conclusions

    Digital phantom simulations have informed an optimized keyhole reconstruction technique for gas exchange images acquired with standard 1‐point Dixon parameters. Our proposed methodology enables more robust quantitative mapping of cardiogenic oscillations, potentially facilitating effective regional quantification of microvascular flow impairment in patients with pulmonary vascular diseases such as CTEPH.

     
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  2. ; ( , Mathematical Finance)
    Abstract

    We consider the optimal investment problem with random endowment in the presence of defaults. For an investor with constant absolute risk aversion, we identify the certainty equivalent, and compute prices for defaultable bonds and dynamic protection against default. This latter price is interpreted as the premium for a contingent credit default swap, and connects our work with earlier articles, where the investor is protected upon default. We consider a multiple risky asset model with a single default time, at which point each of the assets may jump in price. Investment opportunities are driven by a diffusionXtaking values in an arbitrary region. We allow for stochastic volatility, correlation, and recovery; unbounded random endowments; and postdefault trading. We identify the certainty equivalent with a semilinear parabolic partial differential equation with quadratic growth in both function and gradient. Under minimal integrability assumptions, we show that the certainty equivalent is a classical solution. Numerical examples highlight the relationship between the factor process, market dynamics, utility‐based prices, and default insurance premium. In particular, we show that the holder of a defaultable bond has a strong incentive to short the underlying stock, even for very low default intensities.

     
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  3. ; ; ; ; ( , Physics of Plasmas)
  4. ; ; ( , Mathematical Finance)
    Abstract

    This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.

     
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