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1. Market Discipline in the Direct Lending Space

   https://doi.org/10.1093/rfs/hhad081  

   Davydiuk, Tetiana; Marchuk, Tatyana; Rosen, Samuel; Matvos, ed., Gregor (October 2023, The Review of Financial Studies)

   Abstract Using the exclusion of business development companies (BDCs) from stock indexes, this paper studies the effectiveness of market discipline in the direct lending space. Amid share sell-offs by institutional investors, a drop in BDCs’ valuations limits their ability to raise new equity capital. Following this funding shock, BDCs do not adjust their capital structure. At the same time, they are reducing the risk exposure of their portfolios. We document a greater reduction in risk for BDCs subject to stronger market discipline from their debtholders. BDCs pass through the capital shock to their portfolio firms by reducing their investment intensity. 

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2. Open markets

   https://doi.org/10.1111/mafi.12294  

   Karatzas, Ioannis; Kim, Donghan (October 2020, Mathematical Finance)

   Abstract An open market is a subset of a larger equity market, composed of a certain fixed number of top‐capitalization stocks. Though the number of stocks in the open market is fixed, their composition changes over time, as each company's rank by market capitalization fluctuates. When one is allowed to invest also in a money market, an open market resembles the entire “closed” equity market in the sense that the market viability (lack of arbitrage) is equivalent to the existence of a numéraire portfolio (which cannot be outperformed). When access to the money market is prohibited, the class of portfolios shrinks significantly in open markets; in such a setting, we discuss the Capital Asset Pricing Model, how to construct functionally generated portfolios, and the concept of universal portfolio. 

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3. Efficient and Near-Optimal Online Portfolio Selection

   Jézéquel, R; Ostrovskii, D.; Gaillard, P. (October 2022, ArXivorg)

   In the problem of online portfolio selection as formulated by Cover (1991), the trader repeatedly distributes her capital over d assets in each of T>1 rounds, with the goal of maximizing the total return. Cover proposed an algorithm, termed Universal Portfolios, that performs nearly as well as the best (in hindsight) static assignment of a portfolio, with an O(dlog(T)) regret in terms of the logarithmic return. Without imposing any restrictions on the market this guarantee is known to be worst-case optimal, and no other algorithm attaining it has been discovered so far. Unfortunately, Cover's algorithm crucially relies on computing certain d-dimensional integral which must be approximated in any implementation; this results in a prohibitive O(d^4(T+d)^14) per-round runtime for the fastest known implementation due to Kalai and Vempala (2002). We propose an algorithm for online portfolio selection that admits essentially the same regret guarantee as Universal Portfolios -- up to a constant factor and replacement of log(T) with log(T+d) -- yet has a drastically reduced runtime of O(d^(T+d)) per round. The selected portfolio minimizes the current logarithmic loss regularized by the log-determinant of its Hessian -- equivalently, the hybrid logarithmic-volumetric barrier of the polytope specified by the asset return vectors. As such, our work reveals surprising connections of online portfolio selection with two classical topics in optimization theory: cutting-plane and interior-point algorithms. 

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4. Arbitrage theory in a market of stochastic dimension

   https://doi.org/10.1111/mafi.12418  

   Bayraktar, Erhan; Kim, Donghan; Tilva, Abhishek (September 2023, Mathematical Finance)

   Abstract This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements: (i) there exists a supermartingale numéraire portfolio; (ii) each dissected market, which is of a fixed dimension between dimensional jumps, has locally finite growth; (iii) there is no arbitrage of the first kind; (iv) there exists a local martingale deflator; (v) the market is viable. We also present the optional decomposition theorem, which characterizes a given nonnegative process as the wealth process of some investment‐consumption strategy. Furthermore, similar results still hold in an open market embedded in the entire market of stochastic dimension, where investors can only invest in a fixed number of large capitalization stocks. These results are developed in an equity market model where the price process is given by a piecewise continuous semimartingale of stochastic dimension. Without the continuity assumption on the price process, we present similar results but without explicit characterization of the numéraire portfolio. 

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5. Optimal Brokerage Contracts in Almgren–Chriss Model with Multiple Clients

   https://doi.org/10.1137/22M1490156  

   Alvarez, Guillermo Alonso; Nadtochiy, Sergey; Webster, Kevin (September 2023, SIAM Journal on Financial Mathematics)

   This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren-Chriss model. The distinctive features of this work are as follows: (i) the reservation values of the clients are determined endogenously, and (ii) the broker is allowed to not offer a contract to some of the potential clients, thus choosing her portfolio of clients strategically. We find a computationally tractable characterization of the optimal portfolios of clients (up to a digital optimization problem, which can be solved efficiently if the number of potential clients is small) and conduct numerical experiments which illustrate how these portfolios, as well as the equilibrium profits of all market participants, depend on the price impact coefficients. 

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