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Hedging with physical or cash settlement under transient multiplicative price impact Finance Stoch. (IF 1.7) Pub Date : 2024-03-15 Dirk Becherer, Todor Bilarev
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Existence of an equilibrium with limited participation Finance Stoch. (IF 1.7) Pub Date : 2024-02-28 Kim Weston
A limited participation economy models the real-world phenomenon that some economic agents have access to more of the financial market than others. We prove the global existence of a Radner equilibrium with limited participation, where the agents have exponential preferences and derive utility from both running consumption and terminal wealth. Our analysis centers around a coupled quadratic backward
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A framework for measures of risk under uncertainty Finance Stoch. (IF 1.7) Pub Date : 2024-02-07 Tolulope Fadina, Yang Liu, Ruodu Wang
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Optimal consumption and investment with welfare constraints Finance Stoch. (IF 1.7) Pub Date : 2024-02-08
Abstract This paper investigates an optimal consumption and investment problem of an economic agent who faces a welfare constraint: the agent does not accept her expected utility (continuation value) to fall below a certain fixed level regardless of the time and state. This optimisation problem involves an infinite number of constraints. Using a duality approach, we transform infinitely many constraints
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Optimal investment in a large population of competitive and heterogeneous agents Finance Stoch. (IF 1.7) Pub Date : 2024-02-05 Ludovic Tangpi, Xuchen Zhou
This paper studies a stochastic utility maximisation game under relative performance concerns in finite- and infinite-agent settings, where a continuum of agents interact through a graphon (see definition below). We consider an incomplete market model in which agents have CARA utilities, and we obtain characterisations of Nash equilibria in both the finite-agent and graphon paradigms. Under modest
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Arbitrage problems with reflected geometric Brownian motion Finance Stoch. (IF 1.7) Pub Date : 2023-12-20 Dean Buckner, Kevin Dowd, Hardy Hulley
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Faking Brownian motion with continuous Markov martingales Finance Stoch. (IF 1.7) Pub Date : 2023-12-13 Mathias Beiglböck, George Lowther, Gudmund Pammer, Walter Schachermayer
Hamza and Klebaner (2007) [10] posed the problem of constructing martingales with one-dimensional Brownian marginals that differ from Brownian motion, so-called fake Brownian motions. Besides its theoretical appeal, this problem represents the quintessential version of the ubiquitous fitting problem in mathematical finance where the task is to construct martingales that satisfy marginal constraints
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Pricing options on flow forwards by neural networks in a Hilbert space Finance Stoch. (IF 1.7) Pub Date : 2023-11-24 Fred Espen Benth, Nils Detering, Luca Galimberti
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Optimal reinsurance via BSDEs in a partially observable model with jump clusters Finance Stoch. (IF 1.7) Pub Date : 2023-11-17 Matteo Brachetta, Giorgia Callegaro, Claudia Ceci, Carlo Sgarra
We investigate an optimal reinsurance problem when the loss process exhibits jump clustering features and the insurance company has restricted information about the loss process. We maximise expected exponential utility of terminal wealth and show that an optimal strategy exists. By exploiting both the Kushner–Stratonovich and Zakai approaches, we provide the equation governing the dynamics of the
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Dispersion-constrained martingale Schrödinger problems and the exact joint S&P 500/VIX smile calibration puzzle Finance Stoch. (IF 1.7) Pub Date : 2023-11-17 Julien Guyon
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A càdlàg rough path foundation for robust finance Finance Stoch. (IF 1.7) Pub Date : 2023-11-17 Andrew L. Allan, Chong Liu, David J. Prömel
Using rough path theory, we provide a pathwise foundation for stochastic Itô integration which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called property (RIE) for càdlàg paths, which is shown to imply the existence of a càdlàg rough path and of quadratic variation in the
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Optimal investment and consumption for financial markets with jumps under transaction costs Finance Stoch. (IF 1.7) Pub Date : 2023-11-10 Sergei Egorov, Serguei Pergamenchtchikov
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Discount models Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Damir Filipović
Discount is the difference between the face value of a bond and its present value. We propose an arbitrage-free dynamic framework for discount models, which provides an alternative to the Heath–Jarrow–Morton framework for forward rates. We derive general consistency conditions for factor models, and discuss affine term structure models in particular. There are several open problems, and we outline
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A stochastic control perspective on term structure models with roll-over risk Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Claudio Fontana, Simone Pavarana, Wolfgang J. Runggaldier
In this paper, we consider a generic interest rate market in the presence of roll-over risk, which generates spreads in spot/forward term rates. We do not require classical absence of arbitrage and rely instead on a minimal market viability assumption, which enables us to work in the context of the benchmark approach. In a Markovian setting, we extend the control-theoretic approach of Gombani and Runggaldier
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Ruin probabilities for a Sparre Andersen model with investments: the case of annuity payments Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Yuri Kabanov, Platon Promyslov
This note is a complement to the paper (Stoch. Process. Appl. 144:72–84, 2022) by Eberlein, Kabanov and Schmidt on the asymptotics of the ruin probability in a Sparre Andersen non-life insurance model with investments into a risky asset whose price follows a geometric Lévy process. Using techniques from the theory of semi-Markov processes, we extend the result of (Eberlein, Kabanov and Schmidt in Stoch
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In memoriam: Tomas Björk (1947–2021) Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Raquel M. Gaspar, Mariana Khapko
This article celebrates the legacy of Tomas Björk. As we reflect on Tomas’ life and career, we explore his personal and professional journey, highlighting his most significant contributions to mathematical finance.
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Editorial: Special Issue in memory of Tomas Björk Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Martin Schweizer
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Asset pricing with dynamically inconsistent agents Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Mariana Khapko
This paper investigates an endowment economy featuring dynamically inconsistent preferences. Taking a game-theoretic approach, the paper provides an explicit characterisation of the market equilibrium, including the equilibrium short rate, the equilibrium market price of risk and the equilibrium stochastic discount factor. The general results are applied to models featuring non-exponential discounting
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Present-biased lobbyists in linear–quadratic stochastic differential games Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Ali Lazrak, Hanxiao Wang, Jiongmin Yong
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Robust utility maximisation with intractable claims Finance Stoch. (IF 1.7) Pub Date : 2023-09-28 Yunhong Li, Zuo Quan Xu, Xun Yu Zhou
We study a continuous-time expected utility maximisation problem where the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution; hence the name “intractable claim”. In view of the lack of necessary information about the claim, we consider a robust
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Investment–consumption–insurance optimisation problem with multiple habit formation and non-exponential discounting Finance Stoch. (IF 1.7) Pub Date : 2023-09-06 Yike Wang, Jingzhen Liu, Tak Kuen Siu
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Optimal execution with multiplicative price impact and incomplete information on the return Finance Stoch. (IF 1.7) Pub Date : 2023-06-29 Felix Dammann, Giorgio Ferrari
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Fundamental theorem of asset pricing with acceptable risk in markets with frictions Finance Stoch. (IF 1.7) Pub Date : 2023-06-27 Maria Arduca, Cosimo Munari
We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given market. Trading is subject to nonproportional transaction costs and portfolio constraints, and full replication by way of market instruments is not always possible. Rationality is defined in terms of consistency with market prices and acceptable risk thresholds. We obtain a direct
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Contagious McKean–Vlasov systems with heterogeneous impact and exposure Finance Stoch. (IF 1.7) Pub Date : 2023-06-26 Zachary Feinstein, Andreas Søjmark
We introduce a particular heterogeneous formulation of a class of contagious McKean–Vlasov systems, whose inherent heterogeneity comes from asymmetric interactions with a natural and highly tractable structure. It is shown that this formulation characterises the limit points of a finite particle system, deriving from a balance-sheet-based model of solvency contagion in interbank markets, where banks
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Rogue traders Finance Stoch. (IF 1.7) Pub Date : 2023-06-19 Huayuan Dong, Paolo Guasoni, Eberhard Mayerhofer
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A general approach for Parisian stopping times under Markov processes Finance Stoch. (IF 1.7) Pub Date : 2023-06-05 Gongqiu Zhang, Lingfei Li
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Optional projection under equivalent local martingale measures Finance Stoch. (IF 1.7) Pub Date : 2023-03-31 Francesca Biagini, Andrea Mazzon, Ari-Pekka Perkkiö
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A continuous-time model of self-protection Finance Stoch. (IF 1.7) Pub Date : 2023-03-29 Sarah Bensalem, Nicolás Hernández-Santibáñez, Nabil Kazi-Tani
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Market-to-book ratio in stochastic portfolio theory Finance Stoch. (IF 1.7) Pub Date : 2023-03-27 Donghan Kim
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Optimal dividends under a drawdown constraint and a curious square-root rule Finance Stoch. (IF 1.7) Pub Date : 2023-03-24 Hansjörg Albrecher, Pablo Azcue, Nora Muler
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Entropy martingale optimal transport and nonlinear pricing–hedging duality Finance Stoch. (IF 1.7) Pub Date : 2023-03-21 Alessandro Doldi, Marco Frittelli
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Price impact in Nash equilibria Finance Stoch. (IF 1.7) Pub Date : 2023-03-21 Xiao Chen, Jin Hyuk Choi, Kasper Larsen, Duane J. Seppi
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Optimal insurance under maxmin expected utility Finance Stoch. (IF 1.7) Pub Date : 2023-03-14 Corina Birghila, Tim J. Boonen, Mario Ghossoub
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The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. II: Existence, uniqueness and verification for $\vartheta \in (0,1)$ Finance Stoch. (IF 1.7) Pub Date : 2022-12-16 Martin Herdegen, David Hobson, Joseph Jerome
In this article, we consider the optimal investment–consumption problem for an agent with preferences governed by Epstein–Zin (EZ) stochastic differential utility (SDU) over an infinite horizon. In a companion paper Herdegen et al. (Finance Stoch. 27:127–158, 2023), we argued that it is best to work with an aggregator in discounted form and that the coefficients \(R\) of relative risk aversion and
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The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations Finance Stoch. (IF 1.7) Pub Date : 2022-12-16 Martin Herdegen, David Hobson, Joseph Jerome
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Speculative trading, prospect theory and transaction costs Finance Stoch. (IF 1.7) Pub Date : 2022-12-15 Alex S. L. Tse, Harry Zheng
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Mean field portfolio games Finance Stoch. (IF 1.7) Pub Date : 2022-12-13 Guanxing Fu, Chao Zhou
We study mean field portfolio games with random parameters, where each player is concerned with not only her own wealth, but also relative performance to her competitors. We use the martingale optimality principle approach to characterise the unique Nash equilibrium in terms of a mean field FBSDE with quadratic growth, which is solvable under a weak interaction assumption. Motivated by the latter,
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Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models Finance Stoch. (IF 1.7) Pub Date : 2022-12-05 Nicolas Marie
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Optimal execution with stochastic delay Finance Stoch. (IF 1.7) Pub Date : 2022-12-01 Álvaro Cartea, Leandro Sánchez-Betancourt
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Martingale Schrödinger bridges and optimal semistatic portfolios Finance Stoch. (IF 1.7) Pub Date : 2022-11-23 Marcel Nutz, Johannes Wiesel, Long Zhao
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called martingale Schrödinger bridge \(Q_{*}\), that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimisation is shown to be in duality with an exponential utility maximisation over semistatic portfolios. Under
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Jacobi stochastic volatility factor for the LIBOR market model Finance Stoch. (IF 1.7) Pub Date : 2022-09-19 Pierre-Edouard Arrouy, Alexandre Boumezoued, Bernard Lapeyre, Sophian Mehalla
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The characteristic function of Gaussian stochastic volatility models: an analytic expression Finance Stoch. (IF 1.7) Pub Date : 2022-09-16 Eduardo Abi Jaber
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Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation Finance Stoch. (IF 1.7) Pub Date : 2022-09-15 Jorge González Cázares, Aleksandar Mijatović
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Bubbles in discrete-time models Finance Stoch. (IF 1.7) Pub Date : 2022-09-13 Martin Herdegen, Dörte Kreher
We introduce a new definition of bubbles in discrete-time models based on the discounted stock price losing mass under an equivalent martingale measure at some finite drawdown. We provide equivalent probabilistic characterisations of this definition and give examples of discrete-time martingales that are bubbles and others that are not. In the Markovian case, we provide sufficient analytic conditions
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A concept of copula robustness and its applications in quantitative risk management Finance Stoch. (IF 1.7) Pub Date : 2022-09-13 Henryk Zähle
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On ruin probabilities with investments in a risky asset with a regime-switching price Finance Stoch. (IF 1.7) Pub Date : 2022-09-05 Yuri Kabanov, Sergey Pergamenshchikov
We investigate the asymptotics of ruin probabilities when the company invests its reserve in a risky asset with a regime-switching price. We assume that the asset price is a conditional geometric Brownian motion with parameters modulated by a Markov process with a finite number of states. Using techniques from implicit renewal theory, we obtain the rate of convergence to zero of the ruin probabilities
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Semimartingale price systems in models with transaction costs beyond efficient friction Finance Stoch. (IF 1.7) Pub Date : 2022-09-05 Christoph Kühn, Alexander Molitor
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation as they usually appear in frictionless markets. In this paper, we show how the models with and without transaction costs can be unified. The bid and ask prices of a risky asset are given by càdlàg processes
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A class of short-term models for the oil industry that accounts for speculative oil storage Finance Stoch. (IF 1.7) Pub Date : 2022-06-28 Yves Achdou, Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions, Antoine Rostand, José A. Scheinkman
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On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance Finance Stoch. (IF 1.7) Pub Date : 2022-06-28 Søren Asmussen
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Solving optimal stopping problems under model uncertainty via empirical dual optimisation Finance Stoch. (IF 1.7) Pub Date : 2022-06-10 Denis Belomestny, Tobias Hübner, Volker Krätschmer
In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of
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A continuous-time asset market game with short-lived assets Finance Stoch. (IF 1.7) Pub Date : 2022-06-08 Mikhail Zhitlukhin
We propose a continuous-time game-theoretic model of an investment market with short-lived assets. The first goal of the paper is to obtain a stochastic equation which determines the wealth processes of investors and to provide conditions for the existence of its solution. The second goal is to show that there exists a strategy such that the logarithm of the relative wealth of an investor who uses
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A least-squares Monte Carlo approach to the estimation of enterprise risk Finance Stoch. (IF 1.7) Pub Date : 2022-05-13 Hongjun Ha, Daniel Bauer
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Log-optimal and numéraire portfolios for market models stopped at a random time Finance Stoch. (IF 1.7) Pub Date : 2022-05-06 Tahir Choulli, Sina Yansori
This paper focuses on numéraire and log-optimal portfolios when a market model \((S,\mathbb{F},P)\) – specified by its assets’ price \(S\), its flow of information \(\mathbb{F}\) and a probability measure \(P\) – is stopped at a random time \(\tau \). The flow of information that incorporates both \(\mathbb{F}\) and \(\tau \), denoted by \(\mathbb{G}\), is the progressive enlargement of \(\mathbb{F}\)
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Set-valued dynamic risk measures for processes and for vectors Finance Stoch. (IF 1.7) Pub Date : 2022-04-29 Yanhong Chen, Zachary Feinstein
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations are provided. In contrast to scalar risk measures, this equivalence requires an augmentation of the set-valued risk measures for processes. We utilise this result
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Dynamic mean–variance problem with frictions Finance Stoch. (IF 1.7) Pub Date : 2022-03-15 Alain Bensoussan, Guiyuan Ma, Chi Chung Siu, Sheung Chi Phillip Yam
We study a dynamic mean–variance portfolio selection problem with return predictability and trading frictions from price impact. Applying mean-field type control theory, we provide a characterisation of an equilibrium trading strategy for an investor facing stochastic investment opportunities. An explicit equilibrium strategy is derived in terms of the solution to a generalised matrix Riccati differential
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Optimal consumption with reference to past spending maximum Finance Stoch. (IF 1.7) Pub Date : 2022-03-09 Shuoqing Deng, Xun Li, Huyên Pham, Xiang Yu
This paper studies the infinite-horizon optimal consumption problem with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables
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A scaling limit for utility indifference prices in the discretised Bachelier model Finance Stoch. (IF 1.7) Pub Date : 2022-03-01 Asaf Cohen, Yan Dolinsky
We consider the discretised Bachelier model where hedging is done on a set of equidistant times. Exponential utility indifference prices are studied for path-dependent European options, and we compute their non-trivial scaling limit for a large number of trading times \(n\) and when risk aversion is scaled like \(n\ell \) for some constant \(\ell >0\). Our analysis is purely probabilistic. We first
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Scaled insurance cash flows: representation and computation via change of measure techniques Finance Stoch. (IF 1.7) Pub Date : 2022-02-04 Christian Furrer
We consider general multi-state life insurance payment processes and study the expected accumulated cash flows that arise when modifying the payments by scaling factors depending on the time of occurrence of specific events. Such modified payment processes arise naturally in the context of incidental policyholder behaviour. We associate to the modifications new probability measures which allow a standard
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An analytical study of participating policies with minimum rate guarantee and surrender option Finance Stoch. (IF 1.7) Pub Date : 2022-01-28 Maria B. Chiarolla, Tiziano De Angelis, Gabriele Stabile
We perform a detailed theoretical study of the value of a class of participating policies with four key features: (i) the policyholder is guaranteed a minimum interest rate on the policy reserve; (ii) the contract can be terminated by the holder at any time until maturity (surrender option); (iii) at the maturity (or upon surrender), a bonus is credited to the holder if the portfolio backing the policy