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International audienceAs a key problem for multi-sensor attitudedetermination, Wahba’s problem has been studied for almost50 years. Different from existing methods, this paper presentsa novel linear approach to solving this problem. We name theproposed method the Fast Linear Attitude Estimator (FLAE)because it is faster than known representative algorithms. Theoriginal Wahba’s problem is extracted to several 1-dimensionalequations based on quaternions. They are then investigatedwith pseudo-inverse matrices establishing a linear solution to ndimensional equations, which are equivalent to the conventionalWahba’s problem. To obtain the attitude quaternion in a robustmanner, an eigenvalue-based solution is proposed. Symbolicsolutions to the corresponding characteristic polynomial isderived showing higher computation speed. Simulations aredesigned and conducted using test cases evaluated by severalclassical methods e.g. M. D. Shuster’s QUaternion ESTimator(QUEST), F. L. Markley’s SVD method, D. Mortari’s SecondEstimator of the Optimal Quaternion (ESOQ2) and some recentrepresentative methods e.g. Y. Yang’s analytical method andRiemannian manifold method. The results show that FLAEgenerates attitude estimates as accurate as that of severalexisting methods but consumes much less computation time(about 50% of the known best algorithm). Also, to verifythe feasibility in embedded application, an experiment onthe accelerometer-magnetometer combination is carried outwhere the algorithms are compared via C++ programminglanguage. An extreme case is finally studied, revealing a minorimprovement shows more effectiveness in this case inspired byY. Cheng et al

1 This is a substantially revised version of an earlier paper circulated under the title Analytical Approach to the Valuation of American Path-Dependent Options." We a c knowledge comments and suggestions from two anonymous referees that were extremely useful in revising earlier drafts of this paper. We also acknowledge the extensive and detailed comments of the editor, Michael Selby, that helped to improve the paper substantially, in terms of both content and exposition. We thank James Bodurtha, Jr., Young-Ho Eom, Nengjiu Ju, A.R. AbstractIn this paper, we propose an alternative approach for pricing and hedging American barrier options. Speci cally, w e obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call symmetry" relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational e ciency of our method in pricing and hedging American options.Our implementation of the obtained solution indicates that the proposed approach is both e cient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and e ciency. In particular, the method is free of the di culty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.

This article examines the factors driving the borrower's decision to terminate commercial mortgage contracts with the lender through either prepayment or default. Using loan-level data, we estimate prepayment and default functions in a proportional hazard framework with competing risks, allowing us to account for unobserved heterogeneity. Under a strict definition of mortgage default, we do not find evidence to support the existence of unobserved heterogeneity. However, when the definition of mortgage default is relaxed, we do find some evidence of two distinctive borrower groups. Our results suggest that the values of implicit put and call options drive default and prepayment actions in a nonlinear and interactive fashion. Prepayment and default risks are found to be convex in the intrinsic value of call and put options, respectively. Consistent with the joint nature of the two underlying options, high value of the put/call option is found to significantly reduce the call/put risk since the borrower forfeits both options by exercising one. Variables that proxy for cash flow and credit conditions as well as "ex post" bargaining powers are also found to have significant influence upon the borrower's mortgage termination decision. Copyright 2002 American Real Estate and Urban Economics Association.